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].
See this blog post for a distance estimation formula.
- Burning Ship.png
Burning Ship rendered with exterior distance estimation
- Burning Ship (detail).png
Detail of the Burning Ship, showing a
Original Page by Claude