Realtime fractal curve explorer
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Taxonomy of plane-filling curves
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collection of high-res designs on the Internet Archive
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Gallery of fractal curve designs
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     Specimen of the moment
   (100 images: changes every 10 seconds)
   Select to enlarge
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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 |
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The Classic Dragon Curve |
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The Levy C Curve |
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The Koch Snowflake from MathWorld |
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The Sound of Space-filling Curves |
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The Dragon of Eve |
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Connected Fermat Spirals |
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The Gosper Curve |
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The Sierpinski Curve |
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Doug McKenna's Art |
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Fractal Art bt Robert Fathauer |
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Fractal Art by Tony Hanmer |
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Antonio Marquez-Raygoza's huge web page on the Sierpinksi Triangle |
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Fractal Pinwheel Tile by Bandt, Mekhontsev, and Tetenov |
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Jorg Arndt: Plane-filling curves on all uniform grids |
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Smooth curves by Craig Kaplan |
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One of Pat Forster's fractal quilts, inspired by Ventrella's Dragon of Eve |
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Apollonian Gasket by alunw |
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Dragon Curve made with folded paper strips |
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Grammatical Evolution |
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Cyclomers by Stewart Hinsley |
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Nelson Max's film from 1972 |
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Spacefilling Curves |
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Space-filling Trees |
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Branching Patterns |
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spacefillingcurves.org |
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McWorter's Pentigree |
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Fractal circle art from fdecomite |
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Generalized Gosper Curves (Jin Akiyama, Hiroshi Fukuda, Hiro Ito, and Gisaku Nakamura) |
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Boundary of the Dragon Curve (Chang/Zhang) |
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Scott Kim's Fractal Tree |
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The Sierpinski Arrowhead Curve |
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Dragon Curves from Woolly Thoughts |
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Bowyer Curve |
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Cool Curves from Neuro Fuzzy |
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Compendium of Fractal Tilings |
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Fractal Designs by Tony Hammer |
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Aperiodic Tilings by Mark McClure |
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Creating Classic Fractals |
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"Impossible" Fractals |
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Victor Carbajo's L-Systems Fractal Art |
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Applications for Space-Filling Curves |
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Wolter Schraa's Range Fractal |
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Fractal Curves and Dimension, from "Cut the Knot" |
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Peano Curves (from The Geometry Center) |
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Gary Teachout's Space-filling Curves |
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Hans Sagan's book on Space-Filling Curves |
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Aubrey Jaffer's Multi-Dimensional Space-Filling Curves |
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Nasu Dengaku's Space-Filling Curve Art |
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Tom Karzes' Tiling Fratal Curves |
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Fractal jewelry by Dragon Nerd |
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Mark Dow's Beautiful Curves |
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Space-filling curves for spatial data structures (Herman Haverkort & Freek van Waldervee) |
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Space-filling Curves (from Mark C. Chu-Carroll, in Good Math, Bad Math) |
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Beautiful Images by Miqel |
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The amazing mathematical art of Henry Segerman |
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Fractal Materials |
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Dragon Curves by Jos Leys |
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Random Spacefilling by Paul Bourke |
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Tesselation and Spacefilling |
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Gary's Dragons |
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Radix Fractals by William Gilbert |
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Schmidt Arrangements by Katherine E. Stange |
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Branching Snowflake |
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Context-based Space-filling Curves |
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bending Hyperbolic Kaleidoscopes |
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Smooth Koch |
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Cool images by Richard Lewis |
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Henry Segerman Video on Fractal Curves |
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David Mitchell's Lattice Labyrinths |
| Videos about Fractal Curves |
Brainfilling Curves |
Fractal Folding |
The Dragon of Eve |
Vi Hart Squiggles |
Segerman's talk |
Fractal charm: Space filling curves |
Dragon Fractal - Math Guy |
November Colormap |
Growing the Arrowhead Curve |
All Dragon Curves |
Growing the Snowflake Sweep |
Unfolding the Dragon |
This web site was created by
Jeffrey Ventrella.
Email "jeffrey at ventrella dot com" to suggest other links to add.
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