Burning Ship

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The Burning Ship escape-time fractal is formed by iterations of:

[math] X \to X^2 - Y^2 + A \\ Y \to 2 |X| |Y| + B [/math]

where both steps are performed simultaneously. This differs from the Mandelbrot set only by the absolute values in the iteration for [math]Y[/math]. Conventionally it is visualized with the [math]B[/math] axis increasing downwards in image space, which is flipped from traditional representations of the complex plane [math]A+Bi[/math].

Distance estimation

See this blog post for a distance estimation formula.

Pictures


Original Page by Claude