GART

Mandelbrot Set

Iterate z → z² + c in the complex plane. The boundary is infinitely crumpled; zoom is a window onto that edge, drawn as contour lines.

Mandelbrot Set: Iterate z → z² + c in the complex plane. The boundary is infinitely crumpled; zoom is a window onto that edge, drawn as contour lines.Mandelbrot Set: Iterate z → z² + c in the complex plane. The boundary is infinitely crumpled; zoom is a window onto that edge, drawn as contour lines.

About this pattern

Benoît Mandelbrot, 1980

Mandelbrot Set, fractal, drawn by GART: Iterate z → z² + c in the complex plane. The boundary is infinitely crumpled; zoom is a window onto that edge, drawn as contour lines.
Mandelbrot Set · CC BY 4.0

For each complex c, iterate z → z² + c starting at 0. Points that never escape belong to the set. The boundary is a fractal: zoom does not simplify it. GART draws contour lines of the escape-time field, not a filled raster.

TopicsFractal (opens in a new tab)Complex dynamics (opens in a new tab)Mandelbrot set (opens in a new tab)

Behind the mathematics

Benoît Mandelbrot1924–2010

Mandelbrot set and fractal geometry

Polish-born French-American mathematician who coined fractal geometry and connected self-similar mathematics with forms found throughout nature.