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

Topic C6: A Circus -Ternus Target

(LINKING   D12   and   C6)  
This Circus-Ternus-Target  was designed to further explore the cerebral motion-detectors:   neural systems which purportedly also enabled  my subjective  perceptions of the endogenous rotary spiral dynamics. (see D12)
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."

Visual perceptions are attained On-line,  and also off-line as perceptions of intrinsic images.  

Biological spiral wave activities, as  identified in simple  organisms and  in-vitro  neural tissues,  arise  also in  brain tissue.  These activities 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 .
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 .

** -- 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."      


 Edge Detectors

Demonstrates Arnold tongues, Chiral Motion, Contextual Associative Fields and the Kanizsa  An -isotropic Effect


This target design comprises ten concentric rings
with 16 sectors of alternating black and white tiles
within a 14 cm diameter circle; to be viewed at a distance of one half meter.

"Circus Ternus" targets are designed with orbital incremental ratios of 1.00 to 1.60 and are viewed binocularly with hand-held oscillatory motions imposed upon these targets.  Such stimuli readily elicit Arnol'd Tongue Percepts and Illusory Rotary Motions.  These target designs contain concentric circles with 16, 24 or 32 sectors of alternating black and white tiles, tile dimensions increasing as~ a Fibonacci-  areal  series proportionate  with eccentricity.

The angular subtenses of these areas (tiles or elements) are believed proportional to the architectural array of the visual template. The dartboard displays are presented to the observer en face, at a distance of one meter, and thereafter observed with changing ambient luminances and aspect-ratios, and in combinations of rotational frequency when tilted at 45 degrees. (See Topic D 10, the Polar Mandala, represented in the Planforms published by Bressloff in 2002 described by Purkinje as the Rosettfigur; and  with "Radial frequency adaptation.. which ..  suggests polar-based coding of local shape cues." Bell, Dickinson, Badcock (2008). 


Complex hybrid motile patterns appeared in different zones of the circus target, most apparent in its elliptic motions and with oscillations between 1−8 Hz, together with a 45-degree tilt and tip of the hand-held fan. These transformations depend upon velocity, luminance and adaptation. Patterned motions arise from oscillation or linear planar dynamics, their intersections generate resonances and spiral convolutions. 


Meese TS, Anderson SJ. 2002  conclude that the detection of complex motion in human vision requires both cardinal and spiral mechanisms with a half-bandwidth of approximately 46 degrees. Turbine Effects.   Serrano-Pedraza (2007)  presents "Evidence for Reciprocal Antagonism between motion- sensors tuned to coarse and  to fine features."    Confirmed in experiments with orientation-filtered noise that if the 1 cycle/deg noise flickered and the 3 cycles/deg noise moved, the 1 cycle/deg noise ... appeared to move in the opposite direction to the 3 cycles/deg noise even at long durations. These transformations depend upon velocity, luminance and adaptation ..