Improvement of Escape Time Algorithm by No-Escape-Point

摘要

Escape time algorithm is an universal algorithm when creating fractal image. A class of algorithms based on escape time algorithm is wasting-calculation. In this essay, combined with the feature of eventually periodic point of functions, we define a class of points as no-escape point To analyze the shortcomings of the classic algorithm, we improve the escape time algorithm base on the no-escape points. We analyze the algorithm and put forward the best application scope for it. By creating fractal figures, we find figures created by the two algorithms are consistent with each other except a few escape points. We compare the complexity between the two algorithms and find the iteration times by the improved algorithm are less than escape time algorithm when creating the fractal images. We do several experiments and find the improved algorithm is universal and it reduces time wasting.