In this example, we introduce more variability in the probabilities: |

p_{1} = 0.2, p_{2} = 0.25, p_{3} = 0.25,
and p_{4} = 0.3. |

Among other things, the number of values of the probabilities of regions increases more rapidly. |

Smaller regions have smaller probabilities; if these graphs weren't rescalled vertically they would appear to become closer and closer to a flat surface of height 0. Click here for an animation of the first four iterates, all drawn to the same vertical scale. |

For each region we expect that |

prob scales as (side length)^{some power} |

So instead of letting the height of the graph represent the probability of the
region, now we assign height |

Because the probability measures the fraction of the points that occupy a region, we think of this ratio as a dimension. |

Being viewed at the resolution of the side length of the region, this is a coarse Holder exponent; it is also called the coarse dimension. |

Compared with the pictures of the probabilities, perhaps the most noticeable feature is the graphs of the coarse Holder exonent curve in the opposite direction. |

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