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Fractal Geometry

Fractals

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1 The Mandelbrot and Julia sets
2 Sierpinski triangle
3 Fern
4 Spiral
5 Dragon
6 Rotation Numbers and Internal angles ofthe Mandelbrot bulbs
7 The primary Bulbs counting
8 The Secondary Bulbs Symmetry
9 The Third level Bulbs Symmetry
10 Iterations of real function xn+1 = f( xn ) = xn2 + c
11 Bifurcation diagram for quadratic maps
12 The Mandelbrot, Julia and Fatou sets
13 The Julia sets symmetry
14 Iterations of inverse quadratic maps
15 Critical points and Fatou theorem
16 The Fundamental Dichotomy for Julia sets
17 The fixed points and periodic orbits
18 Local dynamics at a fixed point
19 Tangent bifurcations
20 Period doubling bifurcations
 
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