Ghost Bud

[Pauldelbrot]

This is a zoom into the lower left corner of Toxic Spill. The critical point zero has a period-105 bud here; a different critical point is actually studied in this image, so the bud is a "ghost" where this other critical point sometimes goes to the bud-associated attractor instead of to infinity. This produces petal structures in the image, which in some places show the bud's edge, and which is colored using one of the layers with twist coloring.

Two more layers give infinity its colors: one colors low iterations (30 to 200) a green gradient and the other colors high iterations (200 to 30,000) a gold gradient that shades to white. Divergent points with more than 30,000 iterations are white. All convergent points are bluish.

The image took more than half a week to compute, owing to the high iterations (in the tens of thousands throughout much of the blue and gold regions, and up to one billion for a smattering of pixels) and aggressive antialiasing.

This image was also posted as one of my contest images for 2009.

Freely redistributable and usable subject to the Creative Commons Attribution license, version 3.0.

Detailed statistics:
Name: Ghost Bud
Date: March 22, 2009
Fractal: Supernova Mandelbrot set
Location: c-plane; a = 0.61803398, b = 0.01 + 0.89635i
Depth: Shallow
Min Iterations: 54
Max Iterations: 1,000,000,000
Layers: 3
Anti-aliasing: 3x3, threshold 0, depth 2
Preparation time: 15 minutes
Calculation time: four and a half days (2GHz dual-core Athlon XP)