MODULAR WAVE FUNCTIONS

Using the Wolfram Demonstrations app for Modular Arithematic we can generate some interesting and colorful patterns; like this non-restrictive modulo 18, sum of squares operation.

The general look of these patterns reminded me instantly of a sound waves experiment which was popular on YouTube a while back. The experiment shows a layer of salt on a steel plate that is being vibrated by a sonic frequency. When this occurs interesting patterns begin to show.

These patterns have been formulated into a table, reminiscent of modular forms. It is obvious that some of these patterns 6,7 and 7,6 are modulo operations. 6,7 is equivalent to Mod 13, nonrestrictive addition operation.

By overlaying the visual representation of the sound waves with the modulo 18 table, we get a satisfactory match (See below);

Modular arithmetic has always been linked to waveforms, but what I am doing here is trying to demonstrate it visually, as well as mathematically, so that anyone can appreciate it. Furthermore, because modular and elliptic forms are implicated in the make up of matter; via the electron shells (See; Modular Electron Configuration) the electrons themselves must be produced by an equivalent cosmic vibration located within the aether; a concept which science has tersely and inaccurately dismissed.