Kim Young Bong

The Transactions of the Korea Information Processing Society (1994 ~ 2000), Vol. 4, No. 2, pp. 596-605, Feb. 1997
10.3745/KIPSTE.1997.4.2.596,   PDF Download:

Abstract

The dynamic system employing the self-squared function, f(z)=z^2 c, provides the Mandelbrot set which classifies constants c using the divergence of the sequence staring form the origin. To speed-up the generation of Mandelbrot set images, two approaches, called as the divide-and-conquer technique and the traingular boundary tracing technique, have been developed. However, the divide-and-conquer techinque generates sequences of some pixels that do not affect graphical representations of the Mandelbrot set. The triangular boundary tracing technique does not represent some 8-connected components of the Mandelbrot set. In this paper, we propose a new method which solves the 8-connectivity problem of triangular boundary tracing technique. This algorithm considers the divergence for only pixels which are essential to the graphical representation of the Mandelbrot set. It also gives good representations for 8-connected components like hairly structures.

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