Fractal Curves
Brainfilling Curves - A Fractal Bestiary
by Jeffrey Ventrella


Two hundred pages of color images
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     Specimen of the moment    (100 images: changes every 10 seconds)    Select to enlarge
A curve that bends and curls at every level of maginifation is a fractal curve. It has a fractional dimension between 1 and 2, A curve which is so curvey that it essentially visits every point in a planar area is a spacefilling curve, and it defines a continuous mapping from a lower-dimensional space (a line) into a higher-dimensional space (a plane). Its dimension is 2. The fascinating thing about these curves is that they are self-similar and tiling by nature. There are infinitely many ways that fractal curves can be crafted so that they fill space. These ways can be expressed in elegant geometrical rules, as demonstrated by Koch Construction, the application of L-systems to Turtle Geometry, and Iterated Function Systems.

Viewing a space-filling curve with only a few levels of fractal recursion reveals the beautiful logic of its convoluted path. This page is dedicated to the awesome world of fractal curves, and the infinite ways a single curly line can fill the space between 1 and 2 dimensions.



Web sites about fractal curves and related subjects


The Classic Dragon Curve The Levy C Curve The Koch Snowflake from MathWorld


The Gosper Curve The Sierpinski Curve Doug McKenna's Art


Fractal Art bt Robert Fathauer Fractal Art by Tony Hanmer Antonio Marquez-Raygoza's huge web page on the Sierpinksi Triangle


A Quilt by Pat Forster inspired by a Root 17 Curve Apollonian Gasket by alunw Dragon Curve made with folded paper strips


Grammatical Evolution Cyclomers by Stewart Hinsley Nelson Max's film from 1972


Spacefilling Curves Space-filling Trees Branching Patterns by Jeffrey Ventrella


spacefillingcurves.org McWorter's Pentigree Fractal circle art from fdecomite


Generalized Gosper Curves (Jin Akiyama, Hiroshi Fukuda, Hiro Ito, and Gisaku Nakamura) Boundary of the Dragon Curve (Chang/Zhang) Scott Kim's Fractal Tree


The Sierpinski Arrowhead Curve Dragon Curves from Woolly Thoughts Bowyer Curve


Cool Curves from Neuro Fuzzy Compendium of Fractal Tilings Fractal Designs by Tony Hammer


Aperiodic Tilings by Mark McClure Creating Classic Fractals "Impossible" Fractals


Victor Carbajo's L-Systems Fractal Art Applications for Space-Filling Curves Wolter Schraa's Range Fractal


Fractal Curves and Dimension, from "Cut the Knot" Peano Curves (from The Geometry Center) Gary Teachout's Space-filling Curves


Hans Sagan's book on Space-Filling Curves Aubrey Jaffer's Multi-Dimensional Space-Filling Curves Nasu Dengaku's Space-Filling Curve Art


Tom Karzes' Tiling Fratal Curves Fractal jewelry by Dragon Nerd Mark Dow's Beautiful Curves


Space-filling curves for spatial data structures (Herman Haverkort & Freek van Waldervee) Space-filling Curves (from Mark C. Chu-Carroll, in Good Math, Bad Math) Beautiful Images by Miqel


The amazing mathematical art of Henry Segerman Fractal Materials Dragon Curves by Jos Leys


Random Spacefilling by Paul Bourke Tesselation and Spacefilling Gary's Dragons



Videos of Fractal Curves


Brainfilling Curves

Fractal Folding

The Dragon of Eve

Vi Hart Squiggles



Growing the Arrowhead Curve

All Dragon Curves

Growing the Snowflake Sweep

November Colormap



This web site was created by Jeffrey Ventrella. Email "jeffrey at ventrella dot com" to suggest other links to add.