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ELEMENTARY FRACTALS

PART II

EDGAR VALDEBENITO

ABSTRACT

This note presents a collection of elementary Fractals.

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Introduction

Gaston Julia ( 1893 - 1978 ) : Complex dynamics

Figure 1. Fractal – Julia set.

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Some Classic Fractals

Figure 2. Fractal – Penrose Tiling

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Figure 3. Fractal - Crystal

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Figure 3. Fractal - Seaweed

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A Collection of Elementary Fractals

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Figure 4.

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Figure 5.

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Figure 6.

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Figure 7.

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Figure 8.

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Figure 9.

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Figure 10.

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Figure 11.

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Figure 12.

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Figure 13.

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Figure 14.

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Figure 15.

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Figure 16.

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Figure 17.

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Figure 18.

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Figure 19.

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Figure 20.

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Figure 21.

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Figure 22.

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Figure 23.

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Figure 24.

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Figure 25.

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Figure 26.

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Figure 27.

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Figure 28.

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Figure 29.

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Figure 30.

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Figure 31.

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Figure 32.

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Figure 33.

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Figure 34.

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Figure 35.

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Figure 36.

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Figure 37.

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Figure 38.

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Figure 39.

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Figure 40.

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Figure 41.

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Figure 42.

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Figure 43.

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Figure 44.

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Figure 45.

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Figure 46.

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Figure 47.

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Figure 48.

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Figure 49.

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Figure 50.

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Figure 51.

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Figure 52.

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Figure 53.

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Figure 54.

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Figure 55.

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Figure 56.

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Figure 57.

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Figure 58.

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Figure 59.

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Figure 60.

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Figure 61.

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Figure 62.

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Figure 63.

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Figure 64.

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Figure 65.

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Figure 66.

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Figure 67.

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Figure 68.

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Figure 69.

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Figure 70.

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Figure 71.

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Figure 72.

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Figure 73.

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Figure 74.

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Figure 75.

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Figure 76.

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Figure 77.

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Figure 78.

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Figure 79.

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Figure 80.

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Figure 81.

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Figure 82.

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Figure 83.

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Figure 84.

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Figure 85.

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Figure 86.

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Figure 87.

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Figure 88.

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Figure 89.

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Figure 90.

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Figure 91.

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Figure 92.

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Figure 93.

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Figure 94.

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Figure 95.

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Figure 96.

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Figure 97.

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Figure 98.

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Figure 99.

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Figure 100.

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Figure 101.

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Figure 102.

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Figure 103.

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Figure 104.

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Figure 105.

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Figure 106.

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Figure 107.

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Figure 108.

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Figure 109.

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References 1. Barnsley, M.F. and Rising, H.: Fractals Everywhere, 2nd ed. Boston, MA: Academic

Press, 1993.

2. Bunde, A. and Havlin, S.: Fractals and Disordered Systems, 2nd ed. New York: Springer-

Verlag, 1996.

3. Bunde, A. and Havlin, S.: Fractals in Science. New York: Springer-Verlag, 1994.

4. Devaney, R.L.: Complex Dynamical Systems: The Mathematics Behind the Mandelbrot

and Julia Sets. Providence, RI: Amer. Math. Soc., 1994.

5. Mandelbrot, B: Fractals: Form, Chance,& Dimension. San Francisco, CA: W.H. Freeman,

1977.

6. Mandelbrot, B.: The Fractal Geometry of Nature. New York: W.H. Freeman, 1983.

7. Milnor, J.: Dynamics in One Complex Variable: Introductory Lectures, Vieweg,1999.

8. Peitgen, H.-O., Jurgens, H. and Saupe, D.: Chaos and Fractals: New Frontiers of Science.

New York: Springer-Verlag, 1992.

9. Pickover, C.A.: Fractal Horizons: The Future Use of Fractals. New York: St. Martin’s

Press, 1996.