Mandelbrot

The $n$-th iterate of $z \mapsto z^2 + c$ starting from $0$ -- the complex value itself, not an escape count, so the same machinery that draws a zeta function draws this.

Mandelbrot(c, n?)iterates from 0 at the parameter c, n times (default 64), stopping early once it has clearly escaped

Typed signatures

Type	Package	Applies
untyped	analytic	always
(complex, integer) -> real	compute-engine	always

Domain: Elementary functions

Details

• Numeric only -- evaluates under N() or when an operand is inexact; otherwise stays unevaluated.
• Lowers to a compiled real-scalar kernel and to the WGSL mandelbrot shader function for GPU rendering.

Plot

Examples

Basic #

$-1$ is 2-periodic ($0 \to -1 \to 0$), so an even iteration count returns to $0$

live ↗

In$N(\mathrm{Mandelbrot}(-1, 2))$Out$0.0$

About

Examples	1

See also: Julia