Modification of Chaos Game with variation of compression ratio

Abstract

Chaos Game is a form of game drawing a point on a field with certain rules that are repeated iteratively. In general, the new point in the game chaos is the midpoint of the starting point and reference point. The new point is the result of the dilatation with the center of the reference point with a half dilatation factor. The resulting points will form a pattern by paying attention to the nature of self-similarity. This paper will examine the modification of the game chaos rules in generating new points by varying the r compression ratio applied to triangles and rectangles. The compression ratio will be divided into four different intervals. The results of this study indicate that variations in the compression ratio for r = −1, 1orr → +®or 0 < r < 1or −1 < r < 0 do not produce a fractal object, while r > 1or r < −1 will produce a fractal object.