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Mandelbrot Set — A simple iteration creates a boundary with extraordinary detail.
Look closely. Let the image settle.
Fractals & infinity / Late 1970s–1980s

Mandelbrot Set

A simple iteration creates a boundary with extraordinary detail.

TRY THIS

View larger and compare the main shape with the smaller bulbs near its boundary.

FOLLOW THE SOURCES

History, evidence & image credit

THE IMAGE IN THIS ARCHIVE

Created by Wolfgang Beyer with the program Ultra Fractal 3 .

Original file & attribution · CC BY-SA 3.0

Original image downloaded from Wikimedia Commons; the downloaded file is unchanged. Gallery previews may be resized or converted to WebP; animated previews show the first frame.

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Frequently asked questions

What is Mandelbrot Set?

A simple iteration creates a boundary with extraordinary detail.

What should I look for in Mandelbrot Set?

View larger and compare the main shape with the smaller bulbs near its boundary.

What explains Mandelbrot Set?

Starting with z = 0, repeatedly apply z → z² + c. Values of c whose sequences remain bounded belong to the set. Images commonly color the exterior according to escape behavior.

Another way to see it

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Julia Set — Repeated complex mappings produce intricate connected shapes or dust-like sets.

Julia Set

Gaston Julia and Pierre Fatou

Repeated complex mappings produce intricate connected shapes or dust-like sets.

Koch Snowflake — A finite area is enclosed by a boundary that grows without limit.

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Helge von Koch

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Mandelbrot Boundary Detail — A close view reveals spirals, branching filaments, and smaller structures.

Mandelbrot Boundary Detail

Benoît Mandelbrot and researchers in complex dynamics

A close view reveals spirals, branching filaments, and smaller structures.

Mandelbrot Set — A simple iteration creates a boundary with extraordinary detail.

Mandelbrot Set