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Postscriptum
On June 1994 I returned to Geneva to visit my friends and to attend the Dies Academicus where Fernando Vidal was awarded the prestigious Latsis Prize at the University for his book Piaget before Piaget. Also the neuroscientists Jean-Pierre Changeux, Jacques Paillard and Michel Cuénod received honorary degrees. I had the pleasure to talk again with Paillard, who was the first expert to whom I presented my model of the myotatic reflex based on McCulloch-Pitts' neural nets and Piaget's INRC groups (Marseille 1967). This time I shared with him my ideas about intellectual prosthesis. But this is another story (V).
I returned also to the University Library in order to search for more data about my "rediscovery" of fractal eye movements. I could read the most recent investigations without finding any interesting result to add to my old sample of the hyperbolic distribution of saccades and I found few records of free visual search. Strangely enough nobody seemed to discuss the "chaotic path" of saccades!
But I found a most interesting graph in Yarbus's classical book on eye movements. It refers to the microsaccades during fixation on a stationary point. "The image of the point of fixation always remain inside the fovea...the drift speed varied chaotically from zero to approximately 30 minutes of angle per second" (my emphasis, pages 106 and 108). I made a copy of Yarbus figure 54 (fig. 21) and I compared it with Mandelbrot's (1982) figure 255 for a fractional Brown trails of dimension D ~ 1.111 and D ~ 1.4285 (fig. 22).As can be seen the traces are remarkably similar in complexity and shape, thus confirming my first vivid impression some decades ago of a striking analogy between fractals and eye movements.
Two things. First I returned to my original mental image, a pure analogy between graphics. This time at a lesser scale, microsaccades "inside" the field of fixation itself, the duration of a "stopover". A new argument, perhaps, for fractal space-scaling: microsaccades - measured by minutes of angle- compared to macrosaccades - measured by degrees of angle-, or fixation's fields compared to stopover's points. But a new experimental research of microsaccades will be necesssary in order to establish "at that particular scale" an hyperbolic distribution of the "very small" eye movements too. The chaotic behavior of microsaccades in the fixation's field should be carefully analysed.
Second, Yarbus, in retrospect, has given a hint toward the experimental confirmation of fractal time-scaling showing three different records for saccades of 10, 30 and 60 seconds of duration with comparable complexity (fig. 15). The idea of "eye movements as fractals" is still alive.
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THE FRACTAL STORIES
I. The Temperature of Sight.
II. A Study of Mind.
III.Townscape.
IV. Happy Catastrophes.
V. Talents and Handicaps.
VI. Wanderjahre.
VII. Computers & Education
VIII. My Brain.
IX. The Irenic Subject.
X. ABCD.
XI. My Faith.
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