[1] His father was the oldest member of the Williams Brothers, a quartet of musical entertainers, who appeared on recordings, radio, and television, from the late 1930s to the present.Williams's work was originally inspired by the design principles in natural structure systems promoted by R. Buckminster Fuller.

After graduate studies, he joined Dr. Wilson in September 1967 and continued his research into general structure principles in natural systems.

In 1979, Dover Publications published the third edition titled, The Geometrical Foundation of Natural Structure, in its series of classical explanations of science.

He designed and constructed 18,000 square feet (1,700 m2) of these modular, moveable, expandable-contractible enclosures to raise the endangered desert tortoise (Gopherus agassizii) at the Fort Irwin Military Reservation and Edwards Air Force Base in California, USA.

Following the lead of mathematicians L. Fejes Tóth and C. A. Rogers, Williams formalized the concepts underlying Catenatic Geometry.

In The Kiss Catenatic he expanded the concept of small circles covering a sphere to include interconnected platen circuits that model multi-level linked units of the 3-dimensional matrix chain.

[21] In The Integration of Universal Constants Williams presented relationships among numerous diverse subjects: geometric form, color spectrum, the music octave, the periodic table, astronomy, astrology, psychology, tarot, chakras, gender, seasons of the year, among others.