P G D Associate Family

Here is an MPEG animation illustrating that the P, G, and D, triply periodic minimal surfaces are part of the same associate family.


320 by 240 pixel by 400 frame animation

The diagram below illustrates how the P, G, and D surfaces are related by the parameter theta, represented as the counter-clockwise angle from the posotive hoirzontal axis. The two spans in the animation in which theta varies are indicated by the blue and red arcs.

0 and 180 degrees give the P surface, using only the real components of the weierstrass integral. 90 and 270 degrees give the D surface, using only the imaginary components. The G surface is given by combinations of the real and imaginary components which ocur at approximately 51.985 degrees from the real axis.