Movement Timing and Invariance Arise from Several Geometries
Figure 9
Representation of the values of the three functions during the different trials.
The distribution of the functions aggregated over all trials of the same figural form. A point within the triangle gives the values of the
,
and
functions where
. The values of
function for such a point are equal to the area delineated by the small triangle created by passing lines between this specific point and the two bottom vertices. The values of
are equal to the area delineated by the small triangle created by passing lines between this specific point and the left bottom and top vertices. The values of
function are equal to the area delineated by the small triangle created be passing lines between this point and the right bottom and top vertices. For example, a point on the triangle's edge marked by
is a point where
. For a point located at the top vertex
and
. In the center of the triangle
. The color of any point within the large triangle indicates the number of times that that specific combination of
function values was found. A white point shows a combination that did not appear in any of the trials. A dark blue point represents a combination occurring many times. Panel (A) contains all the trials of the drawing of cloverleaves. Panel (B) contains all the trials of the drawing of oblate limaçon. Panel (C) contains all the trials of the drawing of asymmetric lemniscate. Panel (D) contains all the trials of the locomotion of cloverleaves. Panel (E) contains all the trials of the locomotion of oblate limaçon. Panel (F) contains all the trials of the locomotion of asymmetric lemniscate.