From our experience with the fern, we expect to decompose the spiral into a small number of pieces. |
Indeed, two suffice: |
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To determine scalings and angles, we use the method described in Measuring IFS Pieces. |
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Taking the segment ab as the horizontal base, the r scaling factor
of the blue piece is |
The r scaling factor of the red piece
is |
Analogous measurements give |
Taking the point a to be the origin, the red piece is rotated by the angle between ab and ad. |
Finally, the horizontal translation of the blue piece is the length of ac. |
Thus this spiral fractal is generated by these IFS rules. |
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This spiral is a fractal, unlike the simple logarithmic spiral |
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which is not. |
Here are some more examples. |
Return to Natural Fractal Inverse Problems.