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Matematik Seçkileri
Fraktallar
=> 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
Paradokslar
Sayılar Teorisi
Ziyaretçi defteri
 

Strange Attractor

An attracting set that has zero measure in the embedding phase space and has fractal dimension. Trajectories within a strange attractor appear to skip around randomly.

StrangeAttractors1
StrangeAttractors2

A selection of strange attractors for a general quadratic map

x_(n+1) = a_1+a_2x_n+a_3x_n^2+a_4x_ny_n+a_5y_n+a_6y_n^2
(1)
y_(n+1) = a_7+a_8x_n+a_9x_n^2+a_(10)x_ny_n+a_(11)y_n+a_(12)y_n^2
(2)

are illustrated above, where the letters A to Y stand for coefficients of the quadratic from -1.2 to 1.2 in steps of 0.1 (Sprott 1993c). These represent a small selection of the approximately 1.6% of all possible 25^(12) approx 6×10^(16) such maps that are chaotic (Sprott 1993bc).

 

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