Is the fractal dimension of the golden ratio the universal pattern of information?

With the understanding that the universe is composed of cognitive energy organizing itself into nonlinear networks, I would like to propose that the fractal dimension of the golden ratio may represent a universal pattern of information underlying this process. Fractal geometry reveals that what appears as chaos at one scale gives rise to deeper self-similar order across scales, reflecting a deep simplicity at the heart of complexity. The golden ratio, long observed in natural forms and human creation, generates recursive, self-similar structures—most notably through spiral patterns that repeat proportionally at every level. When viewed through the lens of nonlinear mathematics, these patterns suggest not merely aesthetic harmony, but a potential organizing principle embedded within the fabric of living systems themselves.

The golden ratio, through its spiral patterns, creates self-similarity in Euclidian geometry. Nonlinear mathematics describes the patterns and processes that emerge within chaotic systems. Fractal geometry is the dimension of chaos and self-organizing, nonlinear living networks. In Euclidean geometry, the golden ratio generates self-similarity through recursive spiral patterns: at every scale, the same proportional relationship re-emerges. Extending this into fractal geometry, the fractal dimension of the golden ratio encodes that same spiral pattern as a scale-invariant organizing principle. This is what gives the living universe its capacity to self-organize into nonlinear network structures without any central command—the same deep pattern operating across every level of complexity.

A study done by Steven Strogatz looked at the synchronization of networks in three dimensions. What he found supports the existence of spiral patterns within all networks excitations. Strogatz traced spiral patterns in chemical “BZ” reactions that rhythmically alter between sky blue and rusty red dozens of times. These reactions are named for their discoverers, Boris Belousov and Anatol Zhabotinsky.

As Strogatz writes in his fascinating book Sync: The emerging science of spontaneous order:

Spiral waves are now recognized to be a pervasive feature of all chemical, biological, and physical excitable media. . . . The most striking thing about spiral waves is that they seem to be alive (emphasis mine). They are self-sustaining, they don’t need pacemakers. . . . If you watch one in a thin layer of excitable BZ reaction, it looks like a perpetual pinwheel, chasing its tail and regenerating itself endlessly.

For more detail, see The Fractal Dimension of the Golden Ratio: A Unified Pattern of Information