| The research on chaos model was started from during the end of 19th century and the beginning of 20 the century. It is a newly subject and is full of vigour. It draws the outline of a complicated quality world which ordered and unordered follow each other. exactitude and stochastic unite. easiness and complication is consist. With the modern science and technology developed quickly, the chaos goes into every field and stratum, especially after the computer technology appeared and being used popularly. This article uses the Fractal and Lyapunov-Bxponent to analyze and discuss the Iterated Function System. Some fractal pictures were drawn using Matlab. It does the fallowing works:1. It is analyzed that the base theory of IFS. And many characteristics of IFS with probability are researched. So it provides the base of theory for drawing the fractal picture.2 . The existence of period three in the R-dynamical system one discussed. According to the Li Tianyan-York's theory "The period three must implies the chaos". Using the translation rule.3 . Based on Yaupon-Exponent, two kinds of chaos model, one is Mandelbrot set, another is Henon mapping, is analyzed. Father more for these two model how to get from orderly state to chaos is studied.4. The use of chaos in economics is discussed.
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