Cause and origin of moire interferences in recursive processes and with fixed-point and floating-point data types

Abstract

In the calculation of the map of periods of the Mandelbrot Set and working with fixed-point and floating-point real number representation systems, moire interference patterns always appear. These result from the discretization that every computer sets in the finite encoding of its real values. It is not known from which original layers such interferences are obtained and how these initial layers are generated. This article aims at answering these two questions. In order to search these original layers thousands of images —created by means of two different encodings of the real values and with different accuracies— of the map of periods were analyzed. Some points with constant location, called Source Points, around which regular patterns with hyperbolic configuration are generated, were located as well. This answers the questions regarding the cause and origin of moire interferences. Some characteristics of Source Points are described hereinafter. It is also justified why moire interferences in the plane of periods have a hypersensitive behavior. Finally, it is shown how in dynamic systems accuracy does not only affect the precision of results, but also the configuration of the results themselves. The following interesting reflection is, therefore, open to discussion: if the real world should be seen with a fractal way of looking, accuracy configurates then the essence of everything.