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High-Precision Deep Zoom

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Bat Fractal

The Bat Fractal resulted from a coding bug from my first attempt at Newton's method for z3-1=0. Unlike most errors in coding the fractal equations, this one actually looks kind of nice.

The Bat Fractal
Bat Fractal
Bat Fractal

When rendered with no smoothing (top image) it kind of looks like a bat.

The bottom image is the at same coordinates rendered with exponential smoothing.

Bat Fractal Bat Fractal

The top image is a slightly magnified view of the central convergence at z=0.

The bottom image is zooming in a little more in the top part.

Bat Fractal
Bat Fractal

This fountain-spray sort of pattern is what we see when we zoom in. As with most Julia set fractals, there isn't much diversity of structure here.

This fractal, like the Henon map, quickly reduces to a dust of points on magnification.

These two images are exactly the same except for a slight change in the way the fractal data is converted to colors. This is one of the few fractals I've come across that renders well with a simple linear map.

Bat Fractal

This is zooming into a convergence at the top.

Bat Fractal

Here's a slightly more complex structure, but the basic motif is exactly the same.