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This fractal is a Julia set generated by applying Newton’s method to the formula z^4 + -z^2 – 1, and then adding the constant c, c = 0.01 +0.84i. The regions were split by fixed point, and angular decomposition was used.
This fractal was entered in the Fractal ’99 contest. It got a trace amount of votes (to be precise, one point which means one person voted for it for first place). I actually thought last week’s fractal was better, but it got no votes at all.