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in all dimensions. As can be seen from the diagram below, performing this operation with an intermediate iteration of the island leads to a scaled-up version of the next iteration. Repeating this process indefinitely produces a
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In this case both A and B mean to move forward, + means to turn left 60 degrees and - means to turn right 60 degrees - using a "turtle"-style program such as
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of the plane. The curve itself can likewise be extended to an infinite curve filling the whole plane.
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The Gosper curve can also be used for efficient hierarchical hexagonal clustering and indexing.
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The line from the red to the green point shows a single step of the Gosper curve construction
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Uher, Vojtěch; Gajdoš, Petr; Snášel, Václav; Lai, Yu-Chi; Radecký, Michal (28 May 2019).
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335:. In fact, seven copies of the Gosper island can be joined to form a shape that is
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283:. The first few iterations of it are shown below:
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433:"Hierarchical Hexagonal Clustering and Indexing"
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90:The Gosper curve can be represented using an
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279:The space filled by the curve is called the
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255:{\displaystyle B\mapsto +A-BB--B-A++A+B}
186:{\displaystyle A\mapsto A-B--B+A++AA+B-}
1076:List of fractals by Hausdorff dimension
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381:List of fractals by Hausdorff dimension
7:
71:similar in its construction to the
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1058:How Long Is the Coast of Britain?
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478:NEW GOSPER SPACE FILLING CURVES
353:
339:, but scaled up by a factor of
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1082:The Fractal Geometry of Nature
495:Flowsnake by R. William Gosper
204:
135:
1:
1098:Chaos: Making a New Science
23:A fourth-stage Gosper curve
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94:with rules as follows:
1090:The Beauty of Fractals
327:The Gosper Island can
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1036:Lewis Fry Richardson
1031:Hamid Naderi Yeganeh
821:Burning Ship fractal
753:Weierstrass function
491:at Wolfram MathWorld
407:"Peano-Gosper Curve"
198:
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43:, also known as the
794:Space-filling curve
771:Multifractal system
654:Space-filling curve
639:Sierpinski triangle
450:10.3390/sym11060731
405:Weisstein, Eric W.
123:Replacement rules:
63:whose limit set is
61:space-filling curve
16:Space-filling curve
1021:Aleksandr Lyapunov
1001:Desmond Paul Henry
965:Self-avoiding walk
960:Percolation theory
604:Iterated function
545:Fractal dimensions
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111:
86:Lindenmayer system
45:Peano-Gosper Curve
33:
25:
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1064:Coastline paradox
1041:Wacław Sierpiński
1026:Benoit Mandelbrot
950:Fractal landscape
858:Misiurewicz point
763:Strange attractor
644:Apollonian gasket
634:Sierpinski carpet
483:FRACTAL DE GOSPER
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114:{\displaystyle A}
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981:Michael Barnsley
848:Lyapunov fractal
706:Sierpiński curve
659:Blancmange curve
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538:Characteristics
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472:External links
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711:Z-order curve
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681:Hilbert curve
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489:Gosper Island
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69:fractal curve
67:-7. It is a
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1110:Chaos theory
1105:Kaleidoscope
1096:
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1080:
1006:Gaston Julia
986:Georg Cantor
811:Escape-time
743:Gosper curve
742:
691:Lévy C curve
676:Dragon curve
555:Box-counting
460:10084/138899
440:
436:
426:
414:. Retrieved
400:
349:tessellation
326:
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89:
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73:dragon curve
48:
44:
37:Gosper curve
36:
34:
1101:(1987 book)
1093:(1986 book)
1085:(1982 book)
1071:Fractal art
991:Bill Gosper
955:Lévy flight
701:Peano curve
696:Moore curve
582:Topological
567:Correlation
485:(in French)
386:M.C. Escher
41:Bill Gosper
909:Orbit trap
904:Buddhabrot
897:techniques
885:Mandelbulb
686:Koch curve
619:Cantor set
443:(6): 731.
416:31 October
392:References
275:Properties
98:Angle: 60°
53:spoonerism
1016:Paul Lévy
895:Rendering
880:Mandelbox
826:Julia set
738:Hexaflake
669:Minkowski
589:Recursion
572:Hausdorff
411:MathWorld
232:−
226:−
223:−
214:−
205:↦
181:−
151:−
148:−
142:−
136:↦
57:snowflake
49:flowsnake
1125:Category
926:fractals
813:fractals
781:L-system
723:T-square
531:Fractals
437:Symmetry
375:See also
92:L-system
75:and the
59:), is a
47:and the
875:Tricorn
728:n-flake
577:Packing
560:Higuchi
550:Assouad
341:√
337:similar
101:Axiom:
974:People
924:Random
831:Filled
799:H tree
718:String
606:system
1050:Other
333:plane
418:2013
331:the
329:tile
269:Logo
35:The
455:hdl
445:doi
65:rep
55:of
51:(a
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523:e
516:t
509:v
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343:7
250:B
247:+
244:A
241:+
238:+
235:A
229:B
220:B
217:B
211:A
208:+
202:B
178:B
175:+
172:A
169:A
166:+
163:+
160:A
157:+
154:B
145:B
139:A
133:A
109:A
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