# Simple Dynamics vs. Chaos

## Purpose

To present two math models of the possible evolutionary effects on a species resulting from a mutation variable severity.

Traditionally the process of evolution has been thought of as a continuous process of randomly produced adaptations to changes in the environment. Drastic changes in organisms and species would require equally drastic changes in the environment. Accounting for the relatively abrupt extinction of the dinosaurs required an environmental change of cataclysmic proportions.

Recently thinking has changed to account for abrupt changes and extinctions of organisms and species which have no changes in the environment of corresponding magnitude. These new ways of thinking can be loosely grouped under the title of chaos.

A model of a simple dynamic system may be thought of as the application of **x goes to sin x **to a series of randomly chosen variables (seed values) within the range 0 ..... 1 for one thousand iterations.

This is the graph of data points iterated from a seed value of 0.5 . Note the value smoothly approaches zero.

__UNDER CONSTRUCTION__

To run and graph the **dynamic system model click here **__UNDER CONSTRUCTION__

A model of a simple chaotic system may be thought of as the application of **x goes to tan x** to a series of randomly chosen variables (seed values) within the range 0 ..... 1 for one thousand iterations.

This is the graph of data points iterated from a seed value of 0.5 . Note the value approaches zero with occasional chaotic behavior.

__UNDER CONSTRUCTION__

To run and graph the **chaotic system model click here **__UNDER CONSTRUCTION__

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