Controls: Click the canvas to swap between a parabolic grid and the analagous translation grid.
Parabolic Möbius transformations are the generalization of translations in conformal (angle-preserving) geometry. There's a single pole, acting as both a source and a sink. Points are repelled from one side, move along generalized circles and are attracted to the other side.
In the animation above, I make use of two parabolic transformations. The motion of the purple circles is analagous to translation in the x direction. The motion of the green circles is analagous to translation along the y-direction.
This sketch is continuing what I was doing in another repo,
math-notebook, except this time, it's animated! I also am using
Conformal Geometric Algebra
for the math instead of using complex numbers. The results on the
screen are equivalent; the only difference is how the shapes and
transformations are represented in the math/code.