Thursday, October 15, 2026

Polar explorer

Accidentally running a checkerboarded square as a linear polar and then performing a polar to cartesian transformation, with repeats, yields inwardly folding patterns.


polar checkerboard
first

polar checkerboard 2
second

polar checkerboard 3
third

polar checkerboard 4
fourth

polar checkerboard 5
fifth time

The pattern continues to collapse; five steps are enough to see that happen.  

n.b.: Your results will vary with the transformer that is used.


4 comments:

  1. The left side is the inverse of the right side - or maybe the right side is the inverse of the left side?

    ReplyDelete
  2. The first one, when slid by quickly on my mobile device, seems to produce yellow colors in the what are white blocks.

    Anyone else notice this?

    ReplyDelete