Teragon

Polygon with an infinite number of sides

Not to be confused with Tarragon.

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Creating a teragon, the Koch snowflake Horned triangle or teragonic triangle [1] Quadratic Koch island/Minkowski fractal

A teragon is a polygon with an infinite number of sides, the most famous example being the Koch snowflake ("triadic Koch teragon").[dubious – discuss] The term was coined by Benoît Mandelbrot from the words Classical Greek τέρας (teras, monster) + γωνία (gōnía, corner).[2] Typically, a teragon will be bounded by one or more self-similar fractal curves, which are created by replacing each line segment in an initial figure with multiple connected segments, then replacing each of those segments with the same pattern of segments, then repeating the process an infinite number of times for every line segment in the figure.

## Other examples

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The horned triangle, created by erecting a series of smaller triangles on one corner of an equilateral triangle, is another example of a teragon. It is also an example of a rep-tile, or shape that can be completely dissected into smaller copies of itself.

## References

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1. ^ Albeverio, Sergio; Andrey, Sergio; Giordano, Paolo; and Vancheri, Alberto (1997). The Dynamics of Complex Urban Systems, p.222. Springer. ISBN 9783790819373.
2. ^ Larson, Ron; Hostetler, Robert P.; and Edwards, Bruce H. (1998). Calculus, p.546. 6th edition. Houghton Mifflin. ISBN 9780395869741.

## Further reading

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* Mandelbrot, B. B. (1982). The Fractal Geometry of Nature. W.H. Freeman and Company. ISBN 0-7167-1186-9.

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Fractals

Characteristics|

* Fractal dimensions
* Assouad
* Box-counting
* Higuchi
* Correlation
* Hausdorff
* Packing
* Topological
* Recursion
* Self-similarity

Iterated function
system|

* Barnsley fern
* Cantor set
* Koch snowflake
* Menger sponge
* Sierpiński carpet
* Sierpiński triangle
* Apollonian gasket
* Fibonacci word
* Space-filling curve
* Blancmange curve
* De Rham curve
* Minkowski
* Dragon curve
* Hilbert curve
* Koch curve
* Lévy C curve
* Moore curve
* Peano curve
* Sierpiński curve
* Z-order curve
* String
* T-square
* n-flake
* Vicsek fractal
* Gosper curve
* Pythagoras tree
* Weierstrass function

Strange attractor|

* Multifractal system

L-system|

* Fractal canopy
* Space-filling curve
* H tree

Escape-time
fractals|

* Burning Ship fractal
* Julia set
* Filled
* Newton fractal
* Douady rabbit
* Lyapunov fractal
* Mandelbrot set
* Misiurewicz point
* Multibrot set
* Newton fractal
* Tricorn
* Mandelbox
* Mandelbulb

Rendering techniques|

* Buddhabrot
* Orbit trap
* Pickover stalk

Random fractals|

* Brownian motion
* Brownian tree
* Brownian motor
* Fractal landscape
* Lévy flight
* Percolation theory
* Self-avoiding walk

People|

* Michael Barnsley
* Georg Cantor
* Bill Gosper
* Felix Hausdorff
* Desmond Paul Henry
* Gaston Julia
* Niels Fabian Helge von Koch
* Paul Lévy
* Aleksandr Lyapunov
* Benoit Mandelbrot
* Hamid Naderi Yeganeh
* Lewis Fry Richardson
* Wacław Sierpiński

Other|

* Coastline paradox
* Fractal art
* List of fractals by Hausdorff dimension
* The Fractal Geometry of Nature (1982 book)
* The Beauty of Fractals (1986 book)
* Chaos: Making a New Science (1987 book)
* Kaleidoscope
* Chaos theory

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Fractal software

* Digital art
* Graphics software
* Fractal art

Open-source|

* Apophysis
* Blender
* Fractint
* Fyre
* Kalles Fraktaler
* MilkDrop
* Sterling

GNU|

* Electric Sheep
* GIMP
* openPlaG
* XaoS

Freeware|

* IFStile

Retail|

| Cross-platform|

* Bryce
* Maple
* Ultra Fractal
* Wolfram Mathematica

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Windows only|

* VisSim

Scenery generator|

* MojoWorld Generator
* Picogen
* Terragen
* VistaPro

Found objects|

* Burning Ship fractal
* Jerusalem cube
* Julia set
* Mandelbox
* Mandelbrot set
* Mandelbulb

Related|

* Computer-generated imagery
* Fractal compression
* Fractal landscape
* Fractal flame
* Iterated function system
* Mathematical visualization
* Orbit trap

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