6 Computer Models of Chaos
 Much of chaos theory would not be possible without the number crunching power of the computer. In order to view May’s bifurcation diagram to the standard shown in this report requires 5,000 calculations for each point, and to create the 3-dimensional Julia set image required 50,000,000 calculations. While computers can achieve this in a matter of minutes with great accuracy, consider the amount of time and concentration it would take for a human to achieve the same result. Even if someone went to the trouble of doing the calculations, there is a significant possibility that some miscalculation would occur and hence, the entire exercise would be worthless.

Computers, therefore, have played and continue to play a large part in the development of chaos theory, from its discovery by Lorenz and Mandelbrot, to more recent work in modelling insulin secreting cell cooperation and stomach tissue voltage patterns.

The following programmes provide a few basic demonstrations of chaotic behaviour and fractal imagery (see appendix 4 for code).

6.1 Mathematics and Populations

Feedback: Numerically displays iterative, non-linear equation xnext = x * l *(1-x)

Sequential Search Feedback: Graphically displays the iterative non-linear equation xnext = x * l * (1-x) and searches for repeating values. Allows user to enter iterations, search length and delay time.

Sierpinski Triangle: Randomly generates a Sierpinski triangle. Allows user to enter delay time.

6.2 Julia Sets

Julia Sets: Plots a single Julia set. Allows user to enter value for both real and imagery parts of complex number, and iterations.

3-Dimensional Sequential Julia Sets: Plots Julia Sets on a 3-axis complex number plane. Allows user to define increments, value to increment (x or y), no of iterations, contour lines, and initial and ending values.

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