What the Hidden Fractals in Jackson Pollock’s Art Tell Us
Fractals of the fractal dimensions most often found in nature (~1.4) make us happy; we are evolved for exactly those dimensions, found in trees/clouds/…
Taylor calculated that the fractal dimensions of Pollock’s work hovered
close to 1 in the early days of his experimentation, in 1943, which
means they were barely fractal at all. But over the next decade, they
increased regularly, hitting just over 1.7 in 1952, 20-odd years before
Mandelbrot’s seminal work.
Our fractal fluency begins with the movement of our eyes. When we look at a fractal, our eyes trace a fractal trajectory with a dimension of around 1.4 —no matter what the fractal’s dimension is. Nature’s most prevalent fractals share this dimension, falling within a range of 1.3 to 1.5. “If we lived on a planet where 1.8 was prevalent, we would have ended up with an eye trajectory of 1.8,” Taylor says. “Clearly what’s happened is our visual system has evolved.”
And we feel good when we do what we’ve evolved to do.
The fractal dimension of art is not always obvious. The bare-boned Zen meditation garden of Kyoto’s 15th-century Ryoanji Temple, for example, solely of 15 rocks positioned across a rectangular swath of raked gravel. In 2002 a group of researchers decided to investigate the mathematical reason for its appeal to tourists and meditators. Using a technique called medial-axis transformation, they found that the axes of symmetry between the rock clusters formed the fractal contour of a tree. When the rocks were rearranged in computer simulations, that tree-like structure and its meditative effect were lost. “The people who built the temple didn’t know about fractals,” says Sternberg, who was not involved in the study. “But they understood at some unconscious level that placing the rocks in that way made people feel calm.”
In the brain, as in the heart, “just right” means just fractal enough to walk the line between chaos and order.