Homework 7: Physical Modelling
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| **Due Date**: 11:59pm March 2, 2025                                          |
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| Homework should be submitted as a single Jupyter notebook to Dropbox         |
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To do **in advance of this homework**:

* Make sure you have run the code in Allen Downey's Chapter 7 notebook.

Exercises
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Complete the exercises corresponding to Exercise 7.1 and 7.2 in Chapter 7 of
Think Complexity (version 2):

1. In Section 7.6, Downey showed that the Rule 18 CA produces a fractal.
   Can you find other 1-D CAs that produce fractals?

   Note: the ``Cell1D`` object in ``Cell1D.py`` does not wrap around
   from the left edge to the right, which creates artifacts at the
   boundaries for some rules.  You might want to use ``Wrap1D``, which
   is a child class of ``Cell1D`` that wraps around.  It is also defined
   in ``Cell1D.py``.

2. In 1990 Bak, Chen and Tang proposed a cellular automaton that is
   an abstract model of a forest fire.  Each cell is in one of three
   states: empty, occupied by a tree, or on fire.

   The rules of the CA are:

   a. An empty cell becomes occupied with probability *p*.

   b. A cell with a tree burns if any of its neighbors
      is on fire.

   c. A cell with a tree spontaneously burns, with
      probability *f*, even if none of its neighbors is on fire.

   d. A cell with a burning tree becomes an empty cell in the next
      time step.

   Write a program that implements this model.  You might want to inherit
   from ``Cell2D``.  Typical values for the parameters are *p=0.01* and
   *f=0.001*, but you might want to experiment with other values.

   Starting from a random initial condition, run the CA until it reaches
   a steady state where the number of trees no longer increases or
   decreases consistently.

   In steady state, is the geometry of the forest fractal?
   What is its fractal dimension?

Submission
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Please submit a single Jupyter notebook which completes the above exercises,
filling in Allen Downey's Chapter 7 notebook. There are already placeholders
in the notebook for your work.