Fractals & infinity

12 entries

Explore fractal pictures and explanations of the Mandelbrot set, Julia sets, Koch snowflake and more. Discover self-similarity, recursion and infinity. Repeated rules, nested worlds, and intricate boundaries. Mathematical patterns rather than perceptual errors.

Search & sort
M. C. Escher — discover his impossible worlds

The collection

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

Mandelbrot Set

Benoît Mandelbrot; earlier work by Robert Brooks and Peter Matelski

A simple iteration creates a boundary with extraordinary detail.

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.

Koch Snowflake

Helge von Koch

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

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.

Burning Ship Fractal — A variation of complex iteration produces forms reminiscent of ships and towers.

Burning Ship Fractal

Michael Michelitsch and Otto E. Rössler

A variation of complex iteration produces forms reminiscent of ships and towers.

Menger Sponge — A cube is hollowed into a three-dimensional web of repeated openings.

Menger Sponge

Karl Menger

A cube is hollowed into a three-dimensional web of repeated openings.

Heighway Dragon — Repeated right-angle turns fold a simple line into a complex shape.

Heighway Dragon

John Heighway, Bruce Banks, and William Harter

Repeated right-angle turns fold a simple line into a complex shape.

Barnsley Fern — A few transformations generate a surprisingly plant-like form.

Barnsley Fern

Michael Barnsley

A few transformations generate a surprisingly plant-like form.

Hilbert Curve — A line turns through a square with increasingly fine resolution.

Hilbert Curve

David Hilbert

A line turns through a square with increasingly fine resolution.

Apollonian Gasket — Tangent circles fill gaps with smaller and smaller circles.

Apollonian Gasket

Classical circle geometry; later mathematical development

Tangent circles fill gaps with smaller and smaller circles.

Frequently asked questions

What is a fractal?

A fractal is a mathematical structure with detail or related patterns across different scales. Some fractals repeat an exact construction; others show more varied forms of self-similarity.

Are fractals optical illusions?

Not necessarily. Through Mirror includes fractals because their repetition, intricate boundaries and nested patterns challenge visual intuition. Their geometry does not have to create a perceptual error.

What is the Mandelbrot set?

The Mandelbrot set is defined by repeatedly applying a mathematical rule to complex numbers and checking whether the results remain bounded. Images show its intricate boundary and related patterns at different scales.