马蹄映射是具有无穷多个周期点的结构稳定（或Ω稳定）的混沌动力学研究中第一个经典型例子．计算机构造出自相似马蹄映射，并实现了升腾变换，提供了马蹄映射的高维动力性态，并据此计算出马蹄映射Ｃａｎｔｏｒ分形图的混沌分维．本算法理论上适用于ｎ次迭代．同时，马蹄映射产生的Ｃａｎｔｏｒ分形图与Ｍａｎｄｅｌｂｒｏｔ集和Ｊｕｌｉａ集以及其它一些分形图，虽然正式地看来是决定论的后果，实质上可看作一个随机过程的极限． Horseshoe mapping is the first classical example of chaos dynamics with stable structure (or Ω-stable) with an infinite number of periodic points. The computer is constructed from similar horseshoe mapping, and the ascending transformation is realized. The high-dimensional dynamic behavior of the horseshoe mapping is provided, and the chaos fractal dimension of the horseshoe map Cantor fractal is calculated. This algorithm is theoretically applicable to n iterations. At the same time, the Cantor fractal and the Mandelbrot and Julia episodes produced by the horseshoe mapping, while formally appear to be the consequences of determinism, can in essence be regarded as the limits of a stochastic process.