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The universe is full of patterns, but is also full of disorder, chaos, and  randomness. Why is pattern everywhere? What is it, and how do humans recognize it?

As we’ve discussed, spirals (and all patterns) form spontaneously. Whirlpools form automatically in bodies of water and other fluids. The water flowing down the drain always follows a spiral motion. Cold milk poured into hot coffee swirls and curls. Fluids naturally flow in swirls and spirals. It turns out that the same swirls can be seen in wafting plumes of smoke, clouds of dust, and swirling drifts of snowflakes. Dust, snow, water, and fire all share an ability to flow and change shape, and all are composed of free-floating particles. The laws of physics that govern these substances also govern stellar matter: they are the same for cream pouring into a cup of coffee and for gas and dust swirling into a galaxy. Both here at home and out in space, spirals form spontaneously for the same fundamental reasons: everything is spinning, and everything is subject to the laws of gravity.

Patterns & Economy
Nature seeks to accomplish the most "building" with the least energy, and with the most economic use of materials.
Nature is always looking for the tightest fit, the shortest path, the least energy expended.

Nature modifies and adapts it's basic patterns as needed.  Constantly shaping materials to the demands of an every changing environment.  The study of pattern formation is the quest to find the hidden unity that lays under all the modifications and adaptations that are constantly churning out of the natural world.
- Ian Stewart

Why Do Scientists Study Patterns?

The human mind is an indefatigable pattern seeker.  In order to survive in a hostile world, we have evolved sensitivity to patterns, which we use to predict what is going to happen to us. 
Human beings like inventing patterns….Science is about digging out the secret patterns that make the universe tick.  We call these patterns the laws of nature. The most effective way for human beings to think about patterns is to use mathematics.  So we’ve convinced ourselves that the laws of nature are mathematical.
(What Shape is a Snowflake p. 172)
Mathematician & Author Ian Stewart
Pattern Formation
Galaxy Formation

From Chaos to Order

In our universe things often cycle
from chaos to order
and then
back to chaos

Why aren't things perpetually chaotic?
Once things achieve a pattern, why don't they stay orderly?
Computer simulation of Galaxy Formation from NASA website

Did you know that a different mixture of chemical compounds can form, stripes, beat out a pulse, and form symphony of spiral waves?

These patterns are formed by dynamic chemical reactions.  They move, oscillate and pulse into spiral formations.

Learn more from wikipedia:
Belousov-Zhabotinsky reaction

Three dimensional computer simulation of a reaction-diffusion system. A filamentous organizing center emanates "scroll ring" patterns. With permission from Arthur Winfree.