Read the Notes and Credits Click on the green flag. Input a value for R between 0 and 1. Input 0.1 for the seed value. Press Space. You can experiment by varying the seed value for a given R value. You can experiment by varying the parameter R. The following parameters duplicate the graphs on age 176. R = 0.8, seed = 0.4 R = 2.5, seed = 0.1 R = 3.1, seed = 0.1 R = 3.8, seed = 0.05
A cobweb representation of Chaos is pictured on page 176 of James Gleick's book, Chaos - Making a New Science. The equation of the parabola is y =4Rx(1–x) with R a parameter that varies from 0 to 1. This is known as the Logistic Equation and is a simple model of animal population where next year's population is determined by this year's population. Each iteration represents one time period. At certain values of R, the population (x) jumps wildly (chaotically) from one value to another value. If one is a careful observer, one can see 'period doubling' by iterating this equation. See my other Logistic Equation projects: An Abstract Fish Population Model https://scratch.mit.edu/projects/195253979/ Chaos Lurks in y = Rx(1 – x) https://scratch.mit.edu/projects/11173887/ y = Rx(1 – x) As a Time Series https://scratch.mit.edu/projects/195475210/
