Doubled Fours

July 4, 2000

This fractal is a Julia set generated by applying Newton’s method to the formula z^8+ 2 z^4 + 1. This is equal to (z^4 + 1)^2, so there are basically four sets of doubled roots at the four roots of -1, hence the name “doubled fours.” Of course, every root becomes the center of a basin of convergence when you apply Newton’s method. Angular decompositon was used with the resulting image.

“Doubled Fours” parameter file