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At each convex corner of the previous image, place another square, centered at that corner, with half the side length of the square from the previous image.
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is given different values, allomorphs of the T-square appear that are computationally equivalent to the T-square but very different in appearance:
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everywhere in the bigger square, for once a point has been darkened, it remains black for every other iteration; however some points remain white.
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Hamma, Alioscia; Lidar, Daniel A.; Severini, Simone (2010). "Entanglement and area law with a fractal boundary in topologically ordered phase".
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Ahmed, Emad S. (2012). "Dual-mode dual-band microstrip bandpass filter based on fourth iteration T-square fractal and shorting pin".
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Using mathematical induction one can prove that for each n ≥ 2 the number of new squares that are added at stage n equals
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Take the union of the previous image with the collection of smaller squares placed in this way.
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This article is about a two dimensional fractal in mathematics. For other uses, see
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The method of creation is rather similar to the ones used to create a
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The T-square fractal can also be generated by an adaptation of the
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393:= 2 and modular arithmetic means that 3 + 2 = 1, 4 + 2 = 2:
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Sierpiński triangle transforming into a T-square fractal
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Dale, Nell; Joyce, Daniel T.; and Weems, Chip (2016).
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Start with a square. (The black square in the image)
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252:The fractal dimension of the boundary equals
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531:Object-Oriented Data Structures Using Java
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84:Learn how and when to remove this message
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462:T-square fractal and Sierpiński triangle
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1161:List of fractals by Hausdorff dimension
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496:List of fractals by Hausdorff dimension
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138:It can be generated from using this
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1216:Iterated function system fractals
1143:How Long Is the Coast of Britain?
214:Squares branches, related by 1/2
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199:Square branches, related by the
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361:The T-Square and the chaos game
1167:The Fractal Geometry of Nature
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373:and the previous vertex was
1183:Chaos: Making a New Science
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350:{\displaystyle 4*3^{(n-1)}}
241:The T-square fractal has a
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565:10.1103/PhysRevA.81.010102
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21:T-square (disambiguation)
39:This article includes a
123:Algorithmic description
68:more precise citations.
16:Two-dimensional fractal
1175:The Beauty of Fractals
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1116:Hamid Naderi Yeganeh
906:Burning Ship fractal
838:Weierstrass function
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879:Space-filling curve
856:Multifractal system
739:Space-filling curve
724:Sierpinski triangle
468:Sierpiński triangle
227:Sierpinski triangle
1106:Aleksandr Lyapunov
1086:Desmond Paul Henry
1050:Self-avoiding walk
1045:Percolation theory
689:Iterated function
630:Fractal dimensions
502:Toothpick sequence
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41:list of references
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1126:Wacław Sierpiński
1111:Benoit Mandelbrot
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943:Misiurewicz point
848:Strange attractor
729:Apollonian gasket
719:Sierpinski carpet
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1071:Georg Cantor
896:Escape-time
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640:Box-counting
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60:Please help
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1186:(1987 book)
1178:(1986 book)
1170:(1982 book)
1156:Fractal art
1076:Bill Gosper
1040:LĂ©vy flight
786:Peano curve
781:Moore curve
667:Topological
652:Correlation
98:mathematics
66:introducing
994:Orbit trap
989:Buddhabrot
982:techniques
970:Mandelbulb
771:Koch curve
704:Cantor set
514:References
367:chaos game
237:Properties
1101:Paul LĂ©vy
980:Rendering
965:Mandelbox
911:Julia set
823:Hexaflake
754:Minkowski
674:Recursion
657:Hausdorff
580:(2): 617.
337:−
323:∗
295:1.5849...
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268:
154:Image 2:
146:Image 1:
140:algorithm
1210:Category
1011:fractals
898:fractals
866:L-system
808:T-square
616:Fractals
490:See also
389:, where
132:T-square
110:T-square
102:T-square
74:May 2014
960:Tricorn
813:n-flake
662:Packing
645:Higuchi
635:Assouad
377:, then
106:fractal
62:improve
1059:People
1009:Random
916:Filled
884:H tree
803:String
691:system
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508:H tree
247:almost
100:, the
1135:Other
225:or a
47:, or
535:ISBN
500:The
414:vinc
391:vinc
387:vinc
561:doi
453:+ 1
435:+ 0
412:If
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201:1/φ
96:In
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