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.