We started working on creating a software tool to produce `only' Mandelbrot set in color, and ended up creating a software tool capable of evaluating any Mathemati- cal expression, to generate escape time fractals, in any color.
While experimenting with this tool, we came up with heather to unknown, unexplained phenomenon. The phenomenon of shape preserving transform, and the phenomenon of embed- ded inner fractal images, were so fascinating that we tried to explain them, so as to generate a preliminary theoretical basis. The usage of transformation vector to preserve shape and transform any nite truncated polynomial fractal is proven. The dominance phenomenon we borrowed, and reused from Computer Science, and shown that it is a very powerful mechanism to predict existence of embedded inner fractals. While dominance principle shows promise, the principle is fairly new at least in the fractal geometry domain. Further theoretical research work is needed to take the preliminary concepts discussed in this paper, into mainstream fractal geometry.
We would specially like to thank Carl Johansen, whose open sourced Mandelbrot viewer we borrowed as starting point of this project.
Academia is awesome, and unless you are a PHD none listens. Thus, our work - howerver fascinating may be did not receieve any acknowledgment - Invariance And Inner Fractals In Polynomial And Transcendental Fractals
Matters not. Let it be. As Einstein said : Galieo was brilliant, but there was no point for him protecting the truth with a sword. The culture I came from - the ancient verse suggests :
सत्य स्वयँ प्रकाश
Truth would come out, on it's own.
Amen to that.
