Types of Fractals
Sweeps is a name given to base-motif fractals in which the motif is placed differently throughout iteration. There are three ways of placing the motif differently:
1. Use a flipped image of the motif.
2. Use a mirror reflection of the motif.
3. Use a flipped mirror reflection of the motif (same as being rotated 180 degrees).
There are also three methods of creating a sweep:
1. Alternate between normal and modified versions of the motif between different steps
of iteration, but use the same version
of the motif for all line segments.
2. Start with the same version of the motif at all steps of iteration, but alternate the versions between different line segments.
3. Alternate the versions between different line segments and start with different versions at different steps of iteration.
By using different methods, we can create 4 different fractals with the same base and motif:
By using none of the methods above, we get the Levy Curve, which is not a sweep. By using method 1, we get the Cesaro’s Sweep, by using method 2, we get the Dragon Fractal, and by using method 3 we get the Polya’s Sweep: