Hi orda,
I was meaning the mathematics of chaos, which is far from patternless!
There's a famous book you may enjoy by Benoît Mandelbrot called The Fractal Geometry of Nature. The mathematics of chaos undergirds all sorts of structures in the natural world. I find this as close to a unifying magic as you will find in science. And yet, of course, it is mathematical.
Here's just a paragraph from Wikipedia on chaos theory and its connection with fractals:
"The year before, Benoît Mandelbrot found recurring patterns at every scale in data on cotton prices.[47] Beforehand, he had studied information theory and concluded noise was patterned like a Cantor set: on any scale the proportion of noise-containing periods to error-free periods was a constant – thus errors were inevitable and must be planned for by incorporating redundancy.[48] Mandelbrot described both the "Noah effect" (in which sudden discontinuous changes can occur) and the "Joseph effect" (in which persistence of a value can occur for a while, yet suddenly change afterwards).[49][50] This challenged the idea that changes in price were normally distributed. In 1967, he published "How long is the coast of Britain? Statistical self-similarity and fractional dimension", showing that a coastline's length varies with the scale of the measuring instrument, resembles itself at all scales, and is infinite in length for an infinitesimally small measuring device.[51] Arguing that a ball of twine appears to be a point when viewed from far away (0-dimensional), a ball when viewed from fairly near (3-dimensional), or a curved strand (1-dimensional), he argued that the dimensions of an object are relative to the observer and may be fractional. An object whose irregularity is constant over different scales ("self-similarity") is a fractal (for example, the Koch curve or "snowflake", which is infinitely long yet encloses a finite space and has fractal dimension equal to circa 1.2619, the Menger sponge and the Sierpiński gasket). In 1975 Mandelbrot published The Fractal Geometry of Nature, which became a classic of chaos theory. Biological systems such as the branching of the circulatory and bronchial systems proved to fit a fractal model."
http://en.wikipedia.org/wiki/Chaos_theory
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