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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.

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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

 

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This webpage is copyrighted by Freda Auyeung and Jane Panamaneechot (since 2000)