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Famous Fractals

 Von Koch Snowflake: Explanation: 1) Start with a straight line.2) This is the first iteration.3) Each time a line is shown, replace with the design shown in the first iteration.4)... continue the pattern...5) After infinite iterations, the Von Koch Snowflake is shown. Sierpinski Triangle: Explanation: 1) Start with a triangle.2) Connect the midpoint of each side to form a smaller triangle. 3)... continue repeating the pattern...4)After more iterations, you get the Siepinski Triangle A Mandelbrot Figure: Explanation: 1) Start with a straight line.2) This is the first iteration.3) Each time a line is shown, replace with the design shown in the first iteration.4) After infinite iterations, a figure made by Mandelbrot is formed. Other fractals

 The Gingerbread Man: The fractal above was created using the formula (defining X and Y are unnecessary but in the fractal above x=-1 and y=0): Xn = 1 - Yn-1 + | X n-1 | Yn = X n-1 The King's Dream by Clifford Pickover: The fractal above was created using the formula:   xn = sin(yn-1 * b) + c * sin(xn-1 * b)   yn = sin(xn-1 * a) + d * sin(yn-1 * a)Both formulas rely on A, B, C, D as constants: A = -0.66918 B = 2.879879 C = 0.765145 D =0.744728 Click to return to the index page

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