Random Fractals

Self-similarity can be extended to allow the pieces to look like the whole in some sense.

The right window is a rescaling of the x-axis by a factor of 4, and the y-axis by a factor of 2. The right picture has about the same distribution of jumps as the left.

The right window is a rescaling of the x-axis by a factor of 4, and the y-axis by a factor of 4/3. The right picture is flatter than the left.

The right window is a rescaling of the x-axis by a factor of 4, and the y-axis by a factor of 4. The right picture is steeper than the left.

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