In fact, one approach to mathematics is via wondering how the patterns come to be the way they are.
Take the wonderful hexagonal cells made by bees to store honey and put the grubs to bed in. No, the bees don't have built-in rulers and set-squares in their brains to make them that perfect shape.
If you overdo the washing-up liquid and get a mass of bubbles (basically round balls of air held in flexible skins of soapy water) on top, get up close and take a look. Each bubble is forced to adjust to those around squeezing it, and most of them will be hexagons.
Bees buiding cells close together on a flat surface have to adjust the shape to get as many as possible into the space. In a wild honeycomb, they cover whatever surface is naturally there, and while most are hexagonal, there are irregular ones too , to fit irregular spaces.
In a man-made hive, the owner has thoughtfully provided them with a series of flat sheets of wax, hung just the right distance apart for them to build tightly packed cells in a neat honeycomb pattern, and still have headroom (bee-space) to move over the top to feed the grubs and fill the honey cells. Natural behaviour to store as much as possible in the space available.