Visual Memory Research
The Genesis of Mnemonic Visual Systems 
Recurrent Dynamics in Excitable Media

Topic D12: Spiral Wave Dynamics in Neocortex

INTRODUCTION 


Rotating spiral waves are ubiquitous throughout the known cosmos :  their  physics  and functional significance  in biological tissues as yet unresolved .
 
In uni-cellular organisms the spirals apparently relate to locomotion (
Babloyantz 1994) ; spiral activity directs  life-cycles in social amoeba and  in slime- moulds (Winfree  2000).     In higher multi-cellular creatures the  related Turing systems appear to influence integumentary patterning,  developmental  morphology,  and even organogenesis   (Vanag  2004).                  
Investigation of  these waves is of special interest  when the spirals arise in the visual 
pathway,  for  little is understood of  spiral wave functions -.if any -  in the living human brain. 

The 10 Hz- cycling  waves  may  represent  adventitious- markers of on-going  excitatory neural activity,   with  positive or with  adverse effects    Possibly, spirals  modulate our  neuro- syncytial communications  (Ermentrout   2001)  whether of a retinal or a cortical derivation .                                                                                                                                                                            
In 1962  I  experienced some  spontaneous entoptic phenomena: these I  had sketched  and labeled  as " Catherine-  wheels and Standing -waves "; and had  preserved  those contemporary  sketches," ( fig i )  , then  believing them mechanical , arising from vascular turbulences.    When originally  encountered entoptically  in 1962  , these  serendipitous dynamic  phenomena lacked  attribution :  hence   my   correspondence  in 1963   with the  Biophysics  Department at the Mayo Clinic.      

At least ten papers on the Belousov-Zhabotinsky (BZ) reaction were published in Russian before the first in English  in  1967 . At  a  conference  held in Prague in 1968 on Biological and Biochemical Oscillators,  Zhabotinsky presented some of his results. 

The publications  in 1973 finally brought recognition of the BZ reaction to the attention of several Western chemists.

Although spiral waves are ubiquitous features of nature, and have been observed in many biological systems,  their existence and potential function in mammalian cerebral cortex remain uncertain...".. Huang X  2010  ....

                 
                       TURING  Patterns : Formations in Excitable Media : 
                                   Entoptic Perceptions now  reported..    

The  neuro-retina and the brain  ,  as  reaction-diffusion systems,   present  as   polar array templates,  and with  cross-linked lattice - architecture , are   deemed  able to sustain  inculcate imposed-  patterns,  and  the  innate Turing effects .                                                                                                                                                  
Turing  patterns . Occasionally , in  1962 and again in  2004 , I  have witnessed  entopic  displays  of  these  spontaneous  images,  as  first  described  in  my  1963 correspondence with  Dr . E Ackerman  and colleagues  in  Biophysics at  the  Mayo Clinic .      

                        Turing :  the   Primal  Code ?     

 "Once a primitive code appeared it could become more sophisticated through a multi-coding mechanism together with classical Darwinian mechanisms " Conrad M   1982.      The  mechanisms which -  ab  initio  -  generated biological    patterns and structures , are  themselves  tuned  to  sense  the  resonant  natural dynamics  in   the external  environmental  patterns"  .   
"Physiological  mechanisms of neuronal information processing  have been shaped during evolution by a continual interplay between organisms and their sensory surroundings " Kurtz R 2003 . 
   
The  Rotating Spiral Waves are   found in many primitive  life –forms,  and  have been   deemed a  putative  communication-  mechanism.  These  dynamic -rotors  are found also in multi-cellular organisms , and are recorded electronically in mammalian cardiac and neural tissues .    

For several years  I have  documented  the  RSW, which are  found subjectively perceptible.   Seen entoptically as ~ 10 Hz, rotations ,  some  90%   are  levo-rotary  cells, while  only  10% of cells are seen as inward-rotary or dextro-rotary .

These RSW  may arise as  epi-phenomena,  indicating  synaptic hyper-activity yet  serving  no semantic  function,   as  some  may  speculate    
    
The  neuro-retina  itself  represents  a reaction-diffusion system  with cross-linked lattice,  able to sustain some stable or drifting Turing effects. 

"Pattern segmentation in a binary/analog world: unsupervised learning versus memory storing."
Lourenço C, Babloyantz A, Hougardy M.
"The Generation of  Morphogenesis . by  harmonic resonances  " 
         
*     Travelling Waves  ( of Helmholtz ) . These  have been  postulated to  "scan "  the CNS.   As a specific  search-mechanism I doubt this ,  but found  some evidence  that  the passage of  these  bi-phasic   waves, at some   4- second intervals ,   may enhance  alternate aspects of  figure /ground displays   by reversing  the contrasts of some persistent illusory and geometric  engram  images .  [  Topic D 11] 

  *  Solitons… qua  .. 3 D  Target waves ?     I  identify  this  phenomenon with  the finite cellular-  automata  [  see B 5  ]  which ..appear to act as  Lexor /cursors :    commonly of a  one- degree visual- subtense   ( 300 micron   if in the  retina ) . These  active  lexor  entities  are  seen only  as  overlying the  texts  in those lexical engrams  which may appear  briefly  in sleep-to-wake  arousal  epochs .  There is in the literature  no  identification  of  this  phenomenon  as explicit  ;  though  implicit  in Legge's  early  findings . 

Coherent  Lexical  Image  Processings  :  the  acculturated semantic  engram  system ."  " Cultural inventions invade evolutionarily older brain circuits   Dehaene S, Cohen L. 2007
  
Turing - effect  patterns,  and the spiral or quasi-periodic  waves , which are   inherent  in  reaction-diffusion systems,  contribute  to  the generation and  recognition of  patterns and textures, and even   of the  text  letter-forms as now  devised:  orthography  the  prime  exemplar of our  inculcate  pattern- recognition  systems .

Textons and their  Lexors...  see   Essay XI.


TURING  Patterns in excitable media ; Entoptic Perceptions.                                                        

Symmetrical   Oscillating Centers  as  witnessed entoptically  in 1962,   prompted my subsequent enquiries  into  the nature  of  these  dynamic patterns .    Naively , I had assumed that  these   spontaneous  entoptic  patterns, which resembled standing waves and vortices, might  be  arising  from vascular - vibrations  in the retina .  I therefore   wrote  to  biophysicist Eugene Ackerman at the  Mayo  Clinic ,  illustrating  and  describing these several images
"basic patterns and very evanescent ... 
seen occasionally  to occur  spontaneously when the eye is dark- adapted and the observer is suddenly aroused from sleep. The whole field may appear as alternating grey and black  circles of these varying  dispositions."         

These patterns I  then sketched, having kept the illustrations figs. i,   ii .
         

 
  
     This Turing pattern had a 15  degree subtense. 

                                                                                             
Fig. 1 Sketch  made  of an  Entoptic Pattern.  "Very broad lines  , perhaps  300  micron  ,  centered upon  four foci  at    10 degrees or so from fixation ( Fig.1 .b ) ..  Of  this quadrantic  image ;  sometimes only the lower half  would  materialize ".                

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  This  representation reveals a 15 degree subtense from fovea to disc.

Fig ii   My 1962  Sketch  of  the  Entoptic  Pattern  
Legend:  "Nine small active  foci  lie at the intersections between  the octagonal cardinal  radii and each  of two concentric circles of about 10  and 20 degree  isopters . 
Their  offsets  depicted  between  adjacent  inner and outer circles  is  a  topography seen in other  geometric  entoptic images    Tremulous  interference patterns arise at the junctions between the two  incommensurate  oscillating  systems   
Extremely fine , say  30 micron width ... concentric lines  centered upon the fovea, with auxiliary  foci at about  5  and  at  10 degrees  from fixation ".
     
(Huang 2004   since  discerned  spiral centers  of  100 micron,  in  perfused  mammalian   cortex)


Assuming  in 1962  that these  standing waves  or  interference  patterns might arise from micro - vibrations  in the choroido- retinal vasculature  ,  I   wrote in 1963  to  biophysicist  Eugene Ackerman at  Mayo  Clinic  describing these several  images :   
"A  basic pattern  .... very evanescent ..  enduring  <4 seconds. .. seen  occasionally   to occur  spontaneously  when the eye is dark- adapted and the observer is suddenly aroused from sleep ...  the whole field may appear as alternating grey and black  circles of these  varying  dispositions :-                                                                                                                                

1) Extremely fine , say  30 micron width .. concentric lines centered upon the fovea, with auxiliary  foci at about  10 degrees from fixation.. fig i .                                                                        
 
2) Very broad lines  , perhaps  300  micron  ,  centered upon  four foci  at 10 degrees or so from fixation Fig ii . .. of this  quadrantic image ;  sometimes only the lower half  would materialize  ".     [Fig 1 c]                                                                                                                               
3)   Concentric  dark and bright  "  petalloid figures  " , multi-centric and  flickering   Seen only  by toggling a stroboscopic lamp  briskly between  30-40 Hz.                                                                                                                                                                                                                                                                                                         
Sept 13  1963.   Dr. Ackerman  replied that  for the  given  frequencies my  "estimated  wave-lengths (of  30 -300 micron )  are  absurdly short for plane waves of a purely shear or compressional nature ..    although  perhaps  possible with surface waves .  with a low interfacial tension.  "  

My attribution of  the  entoptic  wave phenomena to mechanical  vascular turbulent  patterns was  thereupon  abandoned.

Later  Interpretations  were  made by  Jan.  15  2008.  


fig i )  The Entoptic  encountered in  1962 ,  is  now   deemed  a  Turing  pattern. 
  Scale ;  each depicted   field  ~  30 degree subtense    .


fig ii )  Instability was noted as  a  wavering at intersections of the  local minor- foci  within  the  global, centered  oscillations .
       The ring  of the minor foci appear to be missing  three members ;  this inner circle suggests  a full complement  should  be that of eight nodes   The  placement  of the  three active  nodes seen  in the  outer  circle  is also  consistent with the  Template  geometry  whose  nodes  are in  octagonal- lattice  polar- array. ( see  Topic D10, the mandala  )

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Scroll Waves
 
Assuming  in 1962  that these  standing waves  or  interference  patterns might arise from micro - vibrations  in the choroido- retinal vasculature  ,  I   wrote in 1963  to  biophysicist  Eugene Ackerman at  Mayo  Clinic  describing these several   images :   
  "  A  basic pattern  .... very evanescent ..  enduring  <4 seconds. .. seen  occasionally   to occur  spontaneously  when the eye is dark- adapted and the observer is suddenly aroused from sleep ...  the whole field may appear as alternating grey and black  circles of these  varying  dispositions.
                                                                                                                               

1) Extremely fine, say  30 micron width .. concentric lines centered upon the fovea, with auxiliary  foci at about  10 degrees from fixation.                                                                      
 
2) Very broad lines, perhaps  300  micron  ,  centered upon  four foci  at 10 degrees or so from fixation Fig ii . .. of this  quadrantic image ;  sometimes only the lower half  would materialize". 
                                                                                                                          
3)   Concentric  dark and bright  "  petalloid figures  " , multi-centric and  flickering   Seen only  by toggling a stroboscopic lamp  briskly between  30-40 Hz.                                                                                                                       
 Sept 13  1963.   Dr. Ackerman  replied that  for the  given  frequencies my  "estimated  wave-lengths (of  30 -300 micron )  are  absurdly short for plane waves of a purely shear or compressional nature ..    although  perhaps  possible with surface waves .  with a low interfacial tension.  "  

 My attribution of  the  entoptic  wave phenomena to mechanical  vascular turbulent  patterns was  thereupon  abandoned.


                        Later  Interpretations  were  made by  Jan.  15  2008.  


fig i )  The Entoptic  encountered in  1962 ,  is  now   deemed  a  Turing  pattern. 
  Scale ;  each depicted   field  ~  30 degree subtense    .


fig ii )  Instability was noted as  a  wavering at intersections of the  local minor- foci  within  the  global, centered  oscillations .

The ring  of the minor foci appear to be missing  three members ;  this inner circle suggests  a full complement  should  be that of eight nodes   The  placement  of the  three active  nodes seen  in the  outer  circle  is also  consistent with the  Template  geometry  whose  nodes  are in  octagonal- lattice  polar- array. ( see  Topic D10, the mandala  )

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Observations Feb 12  2000:  I again encountered  subjective  vortices ( Topic D 12 ) while investigating  semantic  hypnopompic  and  recursive  lexical  images.  ( see  Topic  B5).
These semantic  mnemonic  engrams   are  witnessed  briefly  when suddenly aroused from sleep  while  remaining  dark- adapted in a lit ambience). 

                                 
These three figures  appeared simultaneously, evolving from prolate expanding cells.  As expansions ceased, a spindle arose axially, terminating when its height equaled the "radius of the prolate ellipse." 

" Towards nonlinear selection of reaction-diffusion patterns in presence of advection -  a spatial dynamics approach"  Yochelis A, Sheintuch M.2009







(Shows the  Source  of  the  Filament )

These three cells operated synchronously over~  eight  seconds, apparently in a 3-D perspective view  : inexplicable in several regards, and with visual uncertainty as to whether the  spindles arose from RSW or from target cells.                                                             .    

Shortly  thereafter  I  came across  graphic illustrations  and  a  text published  earlier  by Gerhardt , in Science  1900,   These   indicated to me that my1962  entoptic vortices  were reaction -diffusion  phenomena;   and  I  further learned  that the chemical  BZ diffusion reaction  itself was not  widely  published before  1973 , and the   biological spiral waves, 1974, see  Winfree .

The dynamics of   the  1962  entoptics   with the   4- seconds  durations and  the wave- dynamics   are  consistent with  RSW  data  now available : specifically  that of   Huang, X   2004   with the  perfused neo-cortex  mammalian- tissue  preparations,   then  reporting a    4- seconds  longevity   of spiral  waves ,  with rotational  frequencies of   4-14 Hz .

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Turing Patterns

June  5  2002.    Two episodes of  geometric  images were witnessed  with closed lids, and in a room illuminated by flickering TV lighting . ( see  conditions  of  Umbral views;   Essays I c.  , and  in limbo ;  see Essay  VIII a).  
 
Each  of these displays had appeared  to occupy  an entire cognitive perceptual  field. The rough  sketches  and    notes of  these  brief  hypnopompic  phenomenal images  were made rapidly and promptly while still fresh in spatial  memory.  The  topologic  lattice  arrangement of these circles  (as  "eyes, or  target cells")  is  evident,  though slightly mis-aligned in the original  sketch  below.  

 "CHEVRONS  and  CIRCLES  " 

The  original  notes had  indicated:

* A sudden onset  of  a  complete  (field ) resembling a wall-paper of coarse structures 
* Chevrons and disc/circles  of  equal dimensions .. black and white       
* Bi-modal-  TEXTURE . . and  TILES   at  90  degrees only  ..    No overlaps            
* Duration  20 seconds  ?   …                                                                                                          
* Motility ,  none  (of the pattern )  but ..  "  a large  roaming- cursor is  present  "  

This   "large roaming cursor " which  moved  slowly to the right across the lower third of the field, caused  no disturbance of the underlying  pattern . 
                                                         
The top- left  marginal notes  made  Sept 18 2002   suggested that a  noughts -and – crosses percept   might have  generated this display !   however,  " no  x  were seen ,  only  the chevrons . " The dated - note scribbled   in the top left margin  reflects  a later idea ,  that experiences  of  (tic –tac- toe)  relate directly to the most  basic orthographic symbols : noughts or crosses.




--  Perceptions  of  the 1.30  am.  display.   The over- all  impression  of this texture-pattern  at 
was  visually dominated  by the 12  targets  (a  figure-over-ground,   ambiguous  bias  )  .  At no point did the black rings touch the black  bars of the chevrons ;   but  some of the chevrons as here sketched  are  fragmented    The domain  of  a target cell is assumed to be demarcated by its white outer annulus.                             


Monday, June 12, 2006 ;   my 2002   sketched   TURING-  pattern  is  presented  below  in a  computer- graphic version .




--- On the  June 5  2002  display  at 1.30 am ,  these   twelve  identical  circular figures , clearly  resembled  the  so-called  Target- cells -  These  circular  cells   appeared  as  interposed  between  geometrically  anti-thetical  chevrons ; their    linear  configurations were  unfamiliar to me,  other than as  scintillating zig-zags of migraine auras  . 


-Global  Aspect ----In the overall  lattice configuration ,  the centers of the target waves are horizontally  and vertically separated by 20 units,   and  diagonally separated by 15 units .  
These  co-ordinates  operate  globally in Cartesian,   and  locally in  the  polar co-ordinates of each  target  cell. 
Park W,2007   Interconversion  between truncated Cartesian and polar expansions of images. An algorithm is applied to solve the polar-Cartesian interpolation problem (see  my  Topic  F 17. "  Visible Perception of Vestibular Signals,  The Phantom Grid.") 
                                -  Estimated  Metrics  of  Local Elements  


 ---- Local  Features.  Taking as unity  the width of a   linear  bar .. .. this dimension   is  judged  equal to  the width  of each  zone  of the  uniform  concentric  target cells  ...   ..    the diameter of each  target cell  is then  7 units ..( or 9 units  if demarcated by a white zone ).      Thus , for the  chevron –textons  , given  the width  of their equidistant  black  bars also  equaling  one unit , as does the space between them  ( the white bars)    Such a  uniform metric  standard  suggests  that this  Turing pattern  operates  the  same intrinsic wavelength  across  the  full  field , manifesting  in  two modes : either  as  the   chevron  VVV  bars , or as   the  circular O O O  elements .


                           Turing pattern with proportion preservation :


 Ishihara S, Kaneko K.2007  "Turing pattern is one of the most universal mechanisms for pattern formation.    In its standard model the number of stripes changes with the system size, since the wavelength of the pattern is invariant."  

Condat L, Van De Ville D, Forster-Heinlein B   2008   A new grid conversion method is proposed to resample between two 2-D periodic lattices with the same sampling density . 
see Topic 17;   Visible Perception of Vestibular Signals   "The Phantom Grid" 
 


METRICS.   The  field  of  cognitive  view   is estimated  as  30-40 degree of  Angular Subtense ( This measure is  the cognitive lexical  visual field , verified  as  standard in which  Orthographic engrams  are  spatially invariant.   The diameter  of one target  cell  of  the  June 5  2002  display   may thus  approximate a  5 degree  subtense ,  coincident   in scale  with  a Lexor ii .   see  Topic  B 5,   AVB.  

  The  1. 30 am  Event.   The   apparition  of the  " floating- cursor " further  encourages the belief  that  this Turing display/ map   arises upon the same cerebral   "texture – platform " which  supports the  fully  documented  Lexical  engrams  of  Orthographic Texts , which are  seen  with  such  cursor /lexors  Part Two :  AVB.      The  one degree lexor as  is consistently  documented in  my Topic B 5  ,  coincidently has  the same  magnitude   as the inner- zone  of these Turing – target-  cells )  while  Lexor  ii ), has a five degrees subtense. 

- June 5  2002      At 5.20 am , some hours later, the  second  hypnopompic display appeared  in limbo  : this  was "of  high resolution, with rotation of rings , five (large , cellular )  entities  of very , fine grained .., on a  background of  Eigengrau …(  noise,  chaos )  ....  motile rotary discs dominant ...  The   "intrusion , momentarily ,  of a   "stick  element  "  caused no disturbance of the second  display,  but  the  contrast of the stick switched between  black to white as the TV flickered . B/W switching  on  ambient light ..  







After this second display 5.20 am., these   five circular figures were  promptly  sketched, and although  labeled  as  Rotating Scroll rings , they  are  depicted  as  Spiral Waves, not as target cells . 

Their  longevity was not recorded.  The background of  this  5. 20  a m. display appeared amorphous.    The disposition of these five  cells  remained  as if on the 1.30 am. lattice;   their diameters ~ double  the earlier stable target- cell  morphology, with  dynamic spiral rotations.

On close scrutiny  these  5. 20  am.  drawings  may  suggest  levo-rotation  and  outward rotations 

Turing  literature,  well-known to many others, was  unfamiliar to me  before 2003:
 

Wilson MT, Sleigh JW 2007. Turing structures: .. spontaneously crystallize...  into random mazelike.    centimeter-scale spatial patterns... " 

Steyn-Ross ML  2007. "Gap junctions mediate large-scale Turing structures in a mean-field cortex driven by sub-cortical noise"

Steyn-Ross. 2009 "Interaction between the Hopf and Turing instabilities may describe the non-cognitive background or "default" state of the brain,  as observed by BOLD imaging."

Baker TI, Cowan JD.  2009 " Spontaneous pattern formation and pinning in the primary visual cortex.     Turing mechanism to generate patterns of activity." 
( Migraine  auras  in the primary visual cortex. are  hemianopic.  Other geometric patterns of spontaneous brain activity , including the   RSW  are  deemed  global )    

Hernández D, Barrio RA.2007   Soliton Behaviours  in a bistable Reaction Diffusion model .. features of Turing systems :    "  The patterns in two dimensions are particularly interesting because they can present a coherent dynamics with   pseudo  spiral rotations... "
 
IXP - Such  patterns might thus  be witnessed ,  in limbo  (the  arousal from sleep)  as  entoptic engrams which are cycling in slow-wave sleep...  and manifested in a noise-driven cortex."


Zhabotinsky 2008   "Coupled and forced patterns in reaction-diffusion systems "... these patterns can be travelling (e.g. spirals, concentric circles, plane waves) or stationary in space (Turing structures, standing waves).  

Yang L,  Dolnik M, Zhabotinsky AM, Epstein IR.2006.  " Turing patterns beyond hexagons and stripes ". The best known Turing patterns are composed of stripes or simple hexagonal arrangements of spots. 

B. Ermentrout (in a personal communication, 2003) suggested that" increased levels of cortical excitation during the moments right after waking-arousal may play a role in manifesting spiral waves at these times." 

The Turing  patterns,  as seen entoptically in 1962  and  2002,   are  deemed the   precursors of   Pattern Formations  of  Nature.. .and of   Orthography !!   [  as the   basic    xx  oo   xxx :   noughts and crosses  !!  ] 

Hu HX, Ji L, Li QS  2008  " Inward and outward spiral waves as well as inward target waves are induced by local delay feedback in a reaction-diffusion system exhibiting a Turing hexagon pattern spontaneously."

B. Ermentrout  (personal communication .  2004 )   has  "observed ,  but not quantified  such subjective spiral phenomena,  attributing  these  to  cortical events ."  However my   subjective experiences of  spiral cell activities  have  remain  unpublished   
                                                  

The following  list  characterizes  the cellular  prevalences  and  activities  as witnessed  over several years'  entoptic  observations, IXP. .   An  epoch of these " activities i n limbo  status "   may  last  about ~ 20 + seconds , with  each RSW  cell   surviving   1- 4  seconds .

* 90%  of cells  are circular,  and  outwardly - levo-rotating  . 
* Rotations ,  at  about  10 Hz . 
* Elliptical  rotators, 5 % incidence .  seen  only as  horizontal (prolate ) entities  .                    
* Over-lapping cells, seen  rarely:,  and only as Ellipses                                                                  

* Striae.,  the planar wave, packets ,   predominantly  as  oblique or horizontal  patches        
* Inward-  Dextro rotators  ~1 % ,,   may  arise  singly  from a  margin of  these  striae.
* R.  Chiralities   arise from  lower edges  of  oblique L striae,   and vice-versa .
* Twin- spirals ,  rare;  seen  in counter-rotations ,  each twin  inwardly rotating,
 as source and sink on one site.                                                          
* Target  / Ring  waves:~ 5%,  large , solitary; usually   " pop -up  "; no  drifting. 
* " Ladders "  seen as solitary entities  , or  enclosed within  blank Targets                                    
* Turing  patterns  were twice observed . ..
*  Spatiotemporal solitons (vortex tori) .  Spinning  tori may occur . ?   logarithmic spirals .  
Malomed BA, 2002  describes  "  localized spatiotemporal solitons (vortex tori) with vorticity s=1. There is no threshold necessary for the existence of these solitons. They are found to be stable if their energy exceeds a certain critical value, so that the stability domain occupies about 10% of the existence region of the solitons. On the contrary to spatial vortex solitons in the same model, the spatiotemporal ones with s=2 are never stable. These results might open the way for experimental observation of spinning three-dimensional solitons in optical media."                                                                                                                      

 Inward   RSW ;  ABSTRACT.     500  w.     Saturday, November 25, 2006      2/10/2008

In-ward spirals were reported in  non -organic excitable media by Vanag  2002  and by Gong 2003,   but apparently  this  dynamic had not  been noted  in  biological tissues,  neither has an in- vivo  low incidence ( > 10 % )   of  dextral spin been  noted.:   in this  present experiential report those two features   have appeared linked , the  rare inward- spiralings  being  linked 50 %  to the rare dextro-rotators .   
 Winfree  1998   noted  " the recent passage of a traveling wave, and the gradient of stimulus intensity is generated by creating a temporary stimuli on the medium : this mechanism  creates a pair of mirror- image rotors. "  Heterochiral ? . This twinning relates to certain  entoptic findings here reported.

Delay-induced inward and outward spiral waves in oscillatory medium. Hu HX,.2008   " Inward and outward spiral waves as well as inward target waves are induced by local delay feedback in a reaction-diffusion system exhibiting a Turing hexagon pattern spontaneously "  
fig  iv. Mechanically Generated Pattern ,  date uncertain ; not replicated 

Distorted  vortices resulted  from steady oblique pressure on the globe   Site of blind spot indicated by  cross .  Apparently  prolate  drifting ellipses.



Mechanically Generated Pattern. Distorted vortices resulted  from steady  oblique pressure on the globe   Site of blind spot indicated by  cross.   Apparently  prolate  drifting ellipses.

      
Verrier  1997 reviews  the neuro- chemistry when   "  sleep-state- dependent  fluctuations in autonomic nervous system activity may precipitate the onset of major cardiovascular- events " 

In-ward rotating spiral waves were   reported in  non -organic excitable media by Vanag  2002 and by Gong   2003  . 


Winfree  in  1998   noted that   with   " the recent passage of a travelling wave, and the gradient of   stimulus intensity is generated by creating a temporary stimuli on the medium .... this mechanism.then ..creates a pair of mirror image rotors. "  

Reports in vivo:

Helmholtz in  1924   had  described   ": subjective  " blue-band’’  traveling waves of ocular origin,  and  H.R.Wilson,  2001,   reports  visual perception. of  cortical  traveling waves . 

Arising  in the  human  brain , the patterns of  ionic  perturbations such as  auras ,  are  familiar to migraineurs . The  voltage sensitive neurons in the brain are also responsive to  RSW oscillations; and hence  subjectively  perceptible , as also are traveling waves.  Voltage sensitive dyes (VSD ) now   enable photographic  images of  rotating spiral waves in  many excitable biological  media ;  such  data  is  critically studied  in the syncytial  myocardium. .

B . Ermentrout  ( personal communication .2004 )  stated  he "  had  observed ,  but  had not quantified  such  subjective spiral phenomena,   attributing  these  to  cortical events " . However  subjective experiences of  spiral cell activities still  remain  unpublished   .           


State-dependency   The  RSW/oscillons  as  here reported  have been  witnessed  only during the  sleep -to-waking  arousal- status ( tag , in limbo ) : these images  are  discerned  then only with closed lids in a favorable ambient lighting , an  "umbral view " . 

The  brief sleep -to-waking  arousal  events  are accompanied  increased synaptic  activity   and by  the  vigorous neuro-vascular transitions which  take effect  over a few seconds ; briefly triggering the (harmless)  RSW displays.   


Verrier  1997 reviewed  the neuro- chemistry when   "  sleep-state- dependent  fluctuations in autonomic nervous system activity may precipitate the onset of major cardiovascular- events ". 
Siegel J.2004 jsiegel@udel.edu    " the discovery of the ascending reticular activating system (ARAS) as the neural source in the brain stem of the waking state..... showed that the brain- stem activating- system   produced cortical- arousal ..

Entoptic images , RSW.         


The  Rotating Spiral Waves  as demonstrated objectively in neural  tissue preparations  are also subjectively visible  when  arising in the human CNS .. Thousands of these RSW spontaneous reaction -diffusion  cells have been witnessed  by this  observer,  and  many such  events  documented over  a  recent three-year study ;  as  here summarized .  
                            
*     90%  of cells  were  Circular and  outwardly  Levo-rotary   
*      5 %  were Elliptical  rotators,   appeared only as  horizontal (prolate ) entities  .                                                                                             *    Over-lapping cells were seen  rarely:  and only as elliptical morphs .                                                                     *      Striae., planar waves,   predominantly  presented  as oblique or horizontal  patches                                                                 *      Inward  rotators  ~1 % ,   arose  from  the  edges of  these striae.                                                        
 *     R  Chiralities  arose  from  lower edges  of  oblique L striae, and vice-versa .                                                         *     Twin- spirals were  rare;  seen  in counter-rotation ,  each twin  inwardly rotating                                                                        *     Target/ring  waves:~  5%,   large  and solitary ,  usually " popped -up ";   did  not  drift.                                                                      
*      Ladders appeared  as solitary entities  , or were  seen within  blank Targets 
*     Spinning  tori may occur . .                                                                                                                             
*.    Turing  patterns  were twice observed  IXP .. 




Letter to Dr. Eugene Ackerman ,   Biophysicist , Mayo Clinic     WRITTEN 1962 

Dear Dr. Ackerman:

I have some sketchy data on the natural mechanical resonances and vibration modes in vivo which may be of some interest to you.  Perhaps you can further my endeavors.

The vibrations that I observe are apparently engendered by the blood flow in the arterioles  feeding the choroid capillaries, and are manifest subjectively as wave patterns concentric upon these arterial foci and arranged most regularly about the foveola.  They can be seen using a Strobotac over a frequency range 20,00 − 3,400 cpm.  They appear as black arcs oscillating across the white background;  This pattern is invariable.  It is always centered upon the fixation point, some six or so foci lying between fixation and the blind spot, and  arcs  extend over the whole field.

   The same basic array   pattern may occasionally be seen to occur spontaneously; when the eye is dark adapted and the observer suddenly aroused from sleep, the whole field may appear as alternating luminous grey and black circles, of varying dispositions:

1) Extremely fine, say 4 micron width, concentric lines centered upon the foveola; with auxiliary foci at about 10° from fixation, 
2) Very broad lines, perhaps 40 microns  centered upon 4 foci at 10° or so from fixation.  This quadruple figure more common, though sometimes only the lower half may materialize.

It is very evanescent, enduring 4 seconds.  Does the quadruple certification  relate to common vibration orders of any sphere?   Is the concentric multifocus pattern attributable primarily to the anatomy of the arteriolar s debouchments (which are not established histologically at all precisely   Why is the center of the radically symmetrical pattern always the foveola?

The only papers I have read deal with forced externally-applied vibrations.  It appears to me that these intrinsic vibrations ? of cardiac origin, which at the cellular level are of the order of 3,000 cpm , may have considerable physiological interest, and may occur in all  tissues.

To revert to the visual  vibratory  findings :
I am dealing chiefly with shear  waves I suppose?  I understand that resonance frequencies in biological  tissue are considered to be between 700 and 2,100 cpm, 
I do not know the frequency of the standing wave pattern which appear spontaneously in the eye, though I can estimate the internodal distance of the compression waves as from 4 to 40 micron ; the stroboscope determines the vibration frequency count at 3,000 cpm.  But these waves appear more complex than the spontaneous standing waves.  

Am I observing  standing  waves occurring in the choroidal-scleral or choroidal-retinal  interfaces?   I would greatly value some comments from you on these aspects.
                                                                                                            Ida Pearce, MD.

September 13, 1963      Dr. Ackerman responded, concluding  that for my given frequencies, the "estimated wavelengths (of 30–300 microns) are absurdly short for plane waves of a purely sheer or compressional nature … although perhaps possible with surface wave … with a low interfacial tension." 
  
     My erroneous attribution of the entoptic wave phenomena to" turbulent vascular patterns" was thereupon abandoned, and this phenomenon  ignored   for many years.
        The RSW  came  again  my attention  recently;   again emerging only during the arousals  to a fully-awake status.  These brief phenomena coincide with the neurovascular transitions which occur with the increased synaptic activity which briefly triggers the RSW entoptic experiences. The literature on Reaction-diffusion Systems is now extensive;  the  RSW entoptic  experiences are elusive, and  as yet unpublished.    see  Topic D12 ,  AVB 


June 5 2002,  1.30 am.  the  Turing Patterns 
                                          
 " Default  Modes ."  "Widespread functional connectivity and fMRI fluctuations   in human visual cortex...   appear ... in the absence of visual stimulation.   When no stimulus is present, sensory systems manifest a robust level of slow organized fluctuation patterns . " . Nir Y, 2006.


Dickinson JE, Badcock DR.2007                                                                  

Selectivity for coherence in polar orientation in human form vision.

Human visual system  is  tuned for coherence in radial and concentric, and +45 degrees and -45 degrees spiral orientations. It is suggested that sensitivity to +45 degrees and -45 degrees logarithmic spirals serves to disambiguate the sense of spiral form, which would not be uniquely specified by measures of the components of orientation along the radial and concentric directions alone.
 A spiral space is introduced within which radial and concentric patterns are diametrically opposed on one axis    and spirals of +45 degrees and -45 degrees on an orthogonal axis  and it is proposed that these represent cardinal axes for detecting global structure. 
Comparison of the sensitivity tuning functions of the four mechanisms tuned to these axes with sensitivity to simple spiral Glass patterns shows that weighted combinations of output from adjacent pairs of this set of mechanisms are sufficient to account for absolute sensitivity to logarithmic spiral Glass patterns of all intermediate spiral angles.
 Control experiments demonstrate that the combinations are labeled for spiral sense (simple spirals of -22.5 degrees spiral angle can be discriminated from +22.5 degrees spirals at threshold for detection) and that adaptation transfers across quadrants of spiral space (adaptation to spirals of -22.5 degrees results in a decrease in sensitivity to orthogonal +22.5 degrees and -67.5 degrees spirals). Together these observations suggest that sensitivity to spirals in each of the quadrants of spiral space is due to higher order mechanisms reliant on output from 0 degrees , 90 degrees , +45 degrees and -45 degrees cardinal mechanisms. 
                        The Generation of  Morphogenesis .. by   "harmonic resonances   " 


– CREDO ---Those mechanisms which  ab  initio   - generated   organic   patterns and structures ,  are  themselves  tuned  to  sense  the  resonant  natural dynamics  in   the external  environmental  patterns       


. "Physiological  mechanisms of neuronal information processing  have been shaped during evolution by a continual interplay between organisms and their sensory surroundings " Kurtz R 2003. 
      
            Turing  patterns .. I have  very occasionally witnessed   these as                           .  . .      spontaneous  hypnopompic images : but briefly  and  non-replicable . IXP.
                               Turing :  a  Primal  Code ?              July 23, 2008


           The  intra-cellular  Rotating Spiral Waves  found in many  unicellular life –forms  are  deemed   a  communication  mechanism;   these   dynamic rotors  are found also in multi-cellular organisms  and are recorded electronically in mammalian neural tissues .     For several years  I have  documented  those  RSW which are thus subjectively perceptible ,  seen entoptically as  10 Hz, levo-rotary  cells :  these may arise as epi-phenomena  indicating  synaptic hyper-activity, but  serving no semantic  function. 

                                                             SPECULATION
     
Conrad M   1983 ..  "Once a primitive code appeared it could become more sophisticated through a multi-coding mechanism together with classical Darwinian mechanisms " 
  Later publications  encourage the consideration that the recruitment of  Turing - effect  patterns,  and the spiral or quasi-periodic  waves , which are   inherent  in  reaction-diffusion systems ,  may  have  contributed  to  the recognition of  patterns and textures, and even   of the  text  letter-forms as  devised ;  letters now an  exemplar of pattern- recognition . see TEXTONS and LEXORS  ,Essay XI.
 The  neuro-retina  itself  represent  a reaction-diffusion system  with cross-linked lattice,  able to sustain some stable .. or drifting .. Turing effects ?   The ‘bootstrapping principle "  is formulated in terms of the fluctuation-instability- framework ; see Babloyantz..’                               

The Generation of  Morphogenesis .. by  "harmonic resonances  " .
Turing  patterns .. I have  very occasionally  witnessed  as  hypnopompic images ,. but briefly   and  non-replicable.  

*     Travelling Waves  ( of Helmholtz ) . These  waves  have been  postulated to    "scan "  the CNS .  As a specific  search-mechanism I doubt this ,  but find  some evidence  that  the passage of  these  bi-phasic   waves,  at some   4- second intervals ,   may enhance  alternate aspects of  figure/ground displays  by reversing  the contrasts of some persistent illusory and geometric  engram  images .   see [D 11] 

*  4 D     Solitons… qua  .. 3D  Target waves ?      I  identify  this  target - phenomenon with the  finite cellular  automata  [  see B 5  ]  which ..appear to act as  Lexor /cursors ,    commonly of a  one- degree visual- subtense   :  =  300 micron  if  in retina .  These  active  entities  are  seen only  as  overlying the lexical engrams  lp * which also  may appear  briefly  in sleep-to-wake  arousal  epochs .  There is nothing in the literature identifying this  phenomenon as explicit  . 

* Engrams . replicate some  reported   "Eidetic "   image  experiences : 
Miller S, Peacock R.   Evidence for the uniqueness of eidetic imagery.
Percept Mot Skills. 1982 Dec;55(3 Pt 2):1219-33.

Dehaene S, Cohen L. 2007   cultural inventions invade evolutionarily older brain circuits 
 Coherent  Lexical  Image  Processings  :  the  acculturated semantic  engram  system .

                Targeted transfer of solitons in continua and lattices.

  Nistazakis HE, Kevrekidis PG, Malomed BA. 
 
  We propose a robust mechanism of targeted energy transfer along a line, as well as on a surface, in the form of transport of   coherent solitary-wave structures, driven by a moving, spatially localized external ac field ( "arm ") in a lossy- medium.
 The efficiency and robustness of the mechanism are demonstrated analytically and numerically in terms of the nonlinear Schrodinger   (NLS) equation, and broad regions of stable operation are identified in the model's parameter space.
 Direct simulations show that the driving arm can manipulate solitons equally well in a lattice NLS model. A salient feature, which is revealed by simulations and  explained analytically, is a resonant character of the operation of the driving arm in the lattice medium, both integer and fractional   resonances being identified. 

Numerical experiments also demonstrate that the same solitary-wave-transport mechanism works  well in two-dimensional lattice media.

* Engrams. relate  to the  reported  "Eidetic "  image  experiences of 
Miller S, Peacock R. 1982  Evidence for the uniqueness of eidetic imagery.
Percept Mot Skills. 1982 Dec;55(3 Pt 2):1219-33.

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LINKING TOPICS  D12 and C6

                      

        Rotary  Spiral  Motions:  Visual Perceptions Attained  On-Line  and  Also Off-line 

      

Biological spiral wave activities, as  identified in simple  organisms and  in-vitro  neural tissues,   arise  also in  brain tissue,  and  may be detected subjectively as  Rotating  Spiral Waves,  RSW .  These in- vivo  entoptic  phenomena, which  I had   chanced upon in 1962, were  later identified with  the  Belousov and Zhabotinsky reaction-diffusion systems. 

   
The  RSW are  seen entoptically ,  with  multiple discrete   cells  rotating  at about 10 Hz . for  up to 4 sec:   Some cells  reach  diameters up to  3 -4 degree angular subtense      Since their   narrow ,  alternating darker and lighter bands  of a cell,  are  feature-less and putatively are  equidistant ,  how  then can their  rotations  be distinguished and enumerated  ?   

     
This dilemma was addressed  by proposing the  entopic RSW  phenomenal motions  as visually equivalent to those of a spinning top or hula-hoop dancer , ,  as   viewed  while  rotating ,  with the  precessions  only distinguishable with a   meandering  of its  pivotal- point .

    

 Perceptions  of  rotary  motion.  Seiffert  in  1998 , evaluating  perceptions  of  the  exogenous  "minimal displacement of the pattern of annular rotating gratings oscillating at various rates " concluded  that   "the changing  position of features was more readily detected than was velocity."

      

Reciprocal Antagonism    
"Evidence  of   Reciprocal Antagonism
between motion- sensors tuned to
coarse and fine features."
(Serrano-Pedraza I, 2007) 
  

Circus-Ternus-Target  was designed   to  further  explore the common motion-detectors :   neural systems  which purportedly also  enabled  my subjective  perceptions of the  endogenous  rotary spiral dynamics.                                                           

 This concentric geometric array  is  mounted on a hand-held  fan, manipulated with precessing  sinusoidal oscillations between 1-8 Hz,  obtaining ~  45 degree tilt and tip  of  the  target. When  this  Target is  presented  in certain  motions,  arrays  of  Arnol’d Tongues  and  of Turbine Effects  are generated.  These  resonant effects are absent  when  using a mechanical  turntable with the spindle  of the machine aligned with the axial center of the target. 

                                          

Arnol'd Tongues   

Reciprocal Antagonism Resonance


Evidence  of   Reciprocal Antagonism between motion -  sensors tuned to coarse and fine features." ( Serrano-Pedraza I, 2007)   Arnold's Tongues  are  seen  at the lower frequencies;  the "Turbines " appear  with acceleration. Both  effects have  increased  salience  at  low luminances,  and  extended domains with accelerations .  Only  a  meandering, off-axis rotation of the Circus Target elicits  these  resonant Arnol'd Tongues, or of  the  Antagonistic Chiral Motions. Detection of  rotation  of the entoptic  RSW is  deemed  to be  enabled  by  a slight shifting eccentricity, RSW  are known to  meander , either  inward or outwardly;  reportedly the ensuing  chirality  being  contrary  to  that of  the meander. 

"Only  a  meandering, off-axis rotation  presentation  of the Circus Target elicits the perceptions  of  Resonant Arnol'd Tongues, of  Antagonistic Chiral Motions and  of Color Asynchrony:  these effects  had been  unanticipated."  -IXP

Bressloff  1999 -- “Based on anatomical evidence, we assume that the lateral connectivity between hypercolumns exhibits symmetries, rendering it invariant under the action of the Euclidean group E(2), composed of reflections and translations in the plane, and a (novel) shift-twist action.”
  

Dickinson JE, Badcock DR.2007  –"Selectivity for coherence in radial and concentric,  +45 degrees and -45 degrees spiral /polar orientation in human form vision."      

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