Fractal Geometry

Fractal Geometry — as experienced in altered states of consciousness — is one of the most consistently reported visual phenomena of psychedelic experience: intricate, self-similar patterns that repeat at every scale of magnification, unfolding continuously in the visual field with an intricacy that outruns ordinary attention. Where ordinary vision presents a world of discrete objects arranged in space, fractalised vision presents a world in which every surface, every gap between surfaces, and every direction one attends to reveals itself as a further pattern of patterns.

PsychonautWiki's Subjective Effect Index catalogues the phenomenon in considerable detail as geometry, organising it along multiple continuous dimensions: level of intricacy, colour saturation, motion (drifting, breathing, rotating), depth (flat versus three-dimensional versus higher-dimensional), and the fascinating gradient from iconic geometry (recognisable patterns) to semantically saturated geometry (patterns that the experiencer feels are meaningful in ways ordinary imagery is not) to the highest levels, which SEI describes as exposure to the inner mechanics of consciousness itself.

The mathematical concept of the fractal — first named by Benoit Mandelbrot in the 1970s — describes objects with non-integer Hausdorff dimension and characteristic self-similarity across scales. The classic examples (the Mandelbrot set, the Julia sets, the Koch snowflake, the Cantor set) are mathematical objects; but nature is full of approximate fractals (coastlines, blood vessels, lung branches, snowflakes, ferns), and human decorative traditions have discovered fractal-like patterns repeatedly (Islamic geometric ornament, Celtic knotwork, Hindu and Buddhist mandalas). The correspondence between the fractals of contemporary mathematics and the visual signatures of psychedelic experience has become one of the more interesting cross-disciplinary conversations of the past few decades.

Experiencers commonly describe fractal geometry as arriving in specific waves — walls, ceilings, and skin surfaces are common substrates — often accompanied by the sense that the patterns are the underlying pattern of the surface they're seen on, briefly made visible. At the highest levels of intensity the geometry itself takes on the character of a language or a message: patterns that seem to carry semantic content, though the content is typically not translatable into ordinary language. This is the state PsychonautWiki calls perceived exposure to a semantic concept network — one of the most-reported and least-articulable dimensions of the deep psychedelic experience.

Sources:
PsychonautWiki — Geometry
Wikipedia — Fractal