.. Created by Adam Cunnningham on Fri Jun 3 2016. **Cellular Automata** ===================== A *cellular automaton* is a self-contained stylized universe in which space is divided into a regular grid of cells. Each cell has a *state* and a set of close neighbors. Time advances in discrete steps. At each step the state of every cell is updated by a transition rule based only on the states of the cell and its neighbors. The transition rule can be thought of as describing the "laws of physics" for the system that the cellular automaton models. These laws are *local* (dependent only on the cell and its neighbors) and *uniform* (the same for every cell). The cellular automaton described in class has: - A one-dimensional lattice. Each cell has just two neighbors, one on either side. - Four possible cell states, each of which is represented by a different color. - Periodic edge conditions - the rightmost and leftmost cells are neighbors. - A transition rule based purely on the sum of the cell state and those of its neighbors. Report Description ------------------ - Using NumPy arrays and array operations, implement the cellular automaton described in class. Randomly choose the cell states for the first generation. - Use **imshow** to display each new generation of cells below the previous one. Make your own choices for the colors used to indicate the state of each cell. - Experiment with lots of different transition rules, then classify them into a small number of different types based on the long-term behavior of the system. Run each cellular automaton for as many generations as you feel are necessary to see the long-term behavior. - If possible, identify some features of the transition rules that give rise to the different kinds of behavior. .. note:: Show several examples for each class of behavior. The matplotlib **subplot** function may be useful here for displaying many images in a single figure. - If you have time, try to find a rule that will generate an output pattern that is similar to the Textile Cone shell shown below. .. figure:: Textile_cone.jpg :alt: By Photographer: Richard Ling (richard@research.canon.com.au) - Location: Cod Hole, Great Barrier Reef, Australia, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=293495