Footstep Illusion Art: Apparent Rotation Generated by Pure Translation

J Ono1, A Tomoeda2, K Sugihara3

1Meiji University, Japan
2Meiji University / JST, CREST, Japan
3Graduate School of Advanced Math. Sci., Meiji University, Japan

Contact: cs21001@meiji.ac.jp

This paper studies an optical illusion called footsteps illusion evoked by constantly moving objects in front of stripes first found by Anstis in 2001. We consider mechanisms of this illusion, formulate the conditions for maximizing the strength of the illusion, classify the apparent motions into eight patterns according to the widths of a pair of objects and their distance, and create new illusion artworks by combining these eight patterns. Moreover we introduce apparent rotation generated by pure translation. In the case of footsteps illusion, the object is a rectangle. But in the case of apparent rotation, the object is a set of four thin and long rectangles forming a square, and the background is a grid consisting of mutually orthogonal stripe patterns. When the squares move in front of this background, the squares look as if they are rotating. Surprisingly, although the two squares have exactly the same shape, we can place them in such a way that they rotate in opposite directions: one rotates clockwise, while the other rotates anticlockwise. We will discuss why apparent rotation can be generated by pure translation.

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