Charting Trends in the Mandelbrot Set & Showing Their Significance for Cosmology

Abstract

The author has been exploring the Mandelbrot Set in unique ways, for about 30 years, by highlighting areas of the Complex plane where the magnitude of the iterand follows a trend. He discovered the Butterfly figure which appears when one colors in areas where the iterand’s magnitude diminishes monotonically over three iterations, revealing patterns in M that may have significance for theories of Cosmology. The progression of form along either edge from the cusp has an evolutive trend that appears to elucidate the fundamental forces. He published a letter in Amygdala, and had conversations with Benoit Mandelbrot, in the late 1980s. But further advances in Mathematics, since that time, establish the importance of the Mandelbrot Set and affirm the relevance of this line of study to Physics. However; a rigorous presentation of these ideas to the Mathematics and Physics community has not been made, so the material presented here has had limited attention thus far, and much of the territory the author has mapped remains largely unexplored by others. This paper is the first in a series to present this body of research to the larger community.