| Given a function f whose range is contained in its domain, and given a point x0 in the domain of f, we generate a sequence |
| x1, x2, x3, x4 ... |
| by |
| x1 = f(x0), x2 = f(x1), x3 = f(x2), x4 = f(x3), ... |
| Here we find a non-numerical way to generate this sequence, and also some ways to uncover patterns in the sequence. |
| Graphical Iteration is a visual method to generate the sequence x1, x2, x3, ... . |
| Binned Histogram presents a picture of how many points fall into each bin. |
| Time Series is a graph of the values, in the sequence the occur. |
| Return Maps uncover functional relations, when they exist. |
| Bifurcation Diagram catalogs the types of dynamical behavior as a function of the system parameter. |
| Kelly Plot assigns colors to each bin and plots the colors in the orider imposed by the data. Repeating and approximately repeating patterns are revealed by Kelly plots. |
Return to Visualizing Iteration Patterns.