Iterations
Inversion to multiple circles -- 2D dynamics with Jacobian 1 -- playing with Mandelbroit
Iterations — four ways
Iteration creates mathematical toys. We all play with then in our own way. Here are my three favorites. All were done many years ago, often with my students.
Inversion to circles (done with Ken Lao and Alex Brakebill)
Jacobian 1 (partly in collaboration with Jonathan Manson ‘87)
Mucking around with the Mandelbroit set.
Counting and plotting in base 1 + i (originally done in collaboration with Jason Roberts)
The picture on the left was computed by Alex Brakebill (‘93) and made artsy by me. It shows the reflection fractal of a single light source from 3 reflective spheres. The upper right is a detail of an iteration with Jacobian 1 done in BASIC by me as part of work done with Jonathan Manson (‘93). The bottom shows the Mandelbroit set inverted to the unit circle.
