# Burning Ship

The Mandelbrot set plots the fate of $$(x + i y) \to (x + i y)^2 + (a + i b).$$

The Burning Ship plots the fate of $$(x + i y) \to (|x| + i |y|)^2 + (a + i b).$$

The absolute values mean the Burning Ship formula is not analytic. It is continuous, but its derivatives are not continuous everywhere.