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=> Apollonian Gasket
=> Barnsley's Fern
=> Barnsley's Tree
=> Batrachion
=> Blancmange Function
=> Box Fractal
=> Brown Function
=> Cactus Fractal
=> Cantor Dust
=> Cantor Function
=> Cantor Set
=> Cantor Square Fractal
=> Capacity Dimension
=> Carotid-Kundalini Fractal
=> Cesàro Fractal
=> Chaos Game
=> Circles-and-Squares Fractal
=> Coastline Paradox
=> Correlation Exponent
=> Count
=> Cross-Stitch Curve
=> Curlicue Fractal
=> Delannoy Number
=> Dendrite Fractal
=> Devil's Staircase
=> Douady's Rabbit Fractal
=> Dragon Curve
=> Elephant Valley
=> Exterior Snowflake
=> Gosper Island
=> H-Fractal
=> Haferman Carpet
=> Hénon Map
=> Hilbert Curve
=> Householder's Method
=> Ice Fractal
=> Julia Set
=> Koch Antisnowflake
=> Koch Snowflake
=> Lévy Fractal
=> Lévy Tapestry
=> Lindenmayer System
=> Mandelbrot Set
=> Mandelbrot Set Lemniscate
=> Mandelbrot Tree
=> Menger Sponge
=> Minkowski Sausage
=> Mira Fractal
=> Newton's Method
=> Peano Curve
=> Peano-Gosper Curve
=> Pentaflake
=> Plane-Filling Function
=> Pythagoras Tree
=> Randelbrot Set
=> Rep-Tile
=> Reverend Back's Abbey Floor
=> San Marco Fractal
=> Sea Horse Valley
=> Siegel Disk Fractal
=> Sierpiński Arrowhead Curve
=> Sierpiński Carpet
=> Sierpiński Curve
=> Sierpiński Sieve
=> Star Fractal
=> Strange Attractor
=> Tetrix
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Ziyaretçi defteri
 

Hilbert Curve

 
HilbertCurve

A Lindenmayer system invented by Hilbert (1891) whose limit is a plane-filling curve which fills a square. Traversing the polyhedron vertices of an n-dimensional hypercube in Gray code order produces a generator for the n-dimensional Hilbert curve. The Hilbert curve can be simply encoded with initial string "L", string rewriting rules "L" -> "+RF-LFL-FR+", "R" -> "-LF+RFR+FL-", and angle 90 degrees (Peitgen and Saupe 1988, p. 278).

HilbertIICurve

A related curve is the Hilbert II curve, shown above (Peitgen and Saupe 1988, p. 284). It is also a Lindenmayer system and the curve can be encoded with initial string "X", string rewriting rules "X" -> "XFYFX+F+YFXFY-F-XFYFX", "Y" -> "YFXFY-F-XFYFX+F+YFXFY", and angle 90 degrees.

HilbertCurve3D

A three-dimensional analog of the Hilbert curve can also be generated (Trott 2004, pp. 93-97).


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