Ellsworth Kelly

This is not specifically about fractals, but about visual patterns generated by randomness, and other processes. Some of Ellsworth Kelly's Spectrum of Colors ... paintings had colors assigned by intricate mathematical relations, instead of just randomly.
Appearing in works by the cubists, Mondrian, Malevich, Klee, Kelly, and others, the spatial grid is one of the most common features of modern art. Of this grid, Krauss writes, "Flattened, geometricized, ordered, it is anti-natural, anti-mimetic, anti-real. It is what art looks like when it turns its back on nature. (Cowart, pg. 37.) Yet for Ellsworth Kelly, the strongest influence was the topographical grids of the cultivated fields in northern France.
Of Kelly's grid paintings, we are most interested in the series Spectrum of Colors Arranged by Chance. As recorded in his Sketchbook 6, Kelly was influenced by a collection of colored tiles, evidently arranged by chance, of the stern of a moored barge. He destroyed his painting of the tiles, because he felt it was not an improvement over the original. Still grids continued to influence his thinking, even subconsciously, as witnessed by his "automatic" drawing of straight lines (using a ruler, but with eyes closed) often produced gridded patterns. With the addition of randomly colored squares to the grid, Kelly achieved an expression of the dialectic reason (grid) versus passion (colors by chance). Also note Kelly's appreciation for the aesthetic character of chance was heightened by his exposure to John Cage's stochastic music. To again quote Cowart, "It seems odd, in that pre-Fractal/computer/digitizing world of 1951, to try to geometricize irregular organic ephemera." While some of the colored squares were arranged genuinely by chance, Kelly's notebooks reveal for some the colors were assigned by complicated manipulation of numerical sequences and geometric constructions.
Motivated by this observation, physicist David Peak suggested using this assignment of colors as a way to visually assay correlations in numerical data. Simple adaptations of this method are good tools to experiment on the visual signatures of uniform, normal, Brownian, fractional Brownian, and Levy random processes. Differences between chaos and randomness, and ways to recognize scaling, can be explored with this method.
For example, here are Kelly plots driven by
a uniform random sequencea normally distributed sequence
a Brownian sequenceiterates of the logistic map