10176

# Motion/Pursuit Law on Invariant Circles (Visual Depth Perception 4)

This Demonstration computes the motion/pursuit law in the two-dimensional horizontal "fixation plane" of the eyes. The observer is looking mainly at F on the vertical axis, but also sees D as she translates to the right at 6.5 cm/sec (interocular distance per second). The distractor can be moved off the axis around the time zero invariant circle.
We do not know a theoretical explanation for the rough approximation of the peak motion/pursuit law by the 2D relative distance, but this Demonstration compares , , and the 2D signed relative distance, . It also lets you vary time and compare the motion/pursuit law at other times.

### DETAILS

The motion/pursuit ratio at is constant on circles passing through the eye node at time zero and distractor with diameter on the axis. (These circles are similar to the invariant circles for binocular disparity, but slightly different.)
This means that the time zero motion/pursuit law is NOT an especially good indicator of the relative distance between the two-dimensional distractor and fixate, , because you can move quite far from F on this circle with no change in the quantity . If we take the translation of the observer into account, we can show that the peak value of the motion/pursuit law is a good indicator of the relative distance in two dimensions. (It is also likely that the changing value of the motion/pursuit ratio is a cue that the brain could use.)
The Demonstration, "Motion/Pursuit Law in 2D (Visual Depth Perception 3)" (see Related Links) contains additional details.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.