I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid — a term used in this work to denote all of standard geometry — Nature exhibits not simply a higher degree but an altogether different level of complexity … The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous."

Man is the animal that draws lines which he himself then stumbles over. In the whole pattern of civilization there have been two tendencies, one toward straight lines and rectangular patterns and one toward circular lines. There are reasons, mechanical and psychological, for both tendencies. Things made with straight lines fit well together and save space. And we can move easily — physically or mentally — around things made with round lines. But we are in a straitjacket, having to accept one or the other, when often some intermediate form would be better.

People want to see patterns in the world. It is how we evolved. We descended from those primates who were best at spotting the telltale pattern of a predator in the forest, or of food in the savannah. So important is this skill that we apply it everywhere, warranted or not.

The straightening board was created because of warped wood, and the plumb line came into being because of things that are not straight. Rulers are established and ritual and rightness are illuminated because the nature is evil.

When the European looks down on this land, divided into minute lots and cultivated to the last acre, he experiences an initial feeling of familiarity. But the way the colours shade into each other, the irregular outlines of the fields and the rice-swamps which are constantly rearranged in different patterns, the blurred edges which look as if they had been roughly stitched together, all this is part of the same tapestry, but — compared to the clearly defined forms and colours of a European landscape — it is like a tapestry with the wrong side showing.

There is in all things a pattern that is part of our universe. It has symmetry, elegance, and grace — those qualities you find always in that which the true artist captures. You can find it in the turning of the seasons, in the way sand trails along a ridge, in the branch clusters of the creosote bush or the pattern of its leaves. We try to copy these patterns in our lives and our society, seeking the rhythms, the dances, the forms that comfort. Yet, it is possible to see peril in the finding of ultimate perfection. It is clear that the ultimate pattern contains its own fixity. In such perfection, all things move toward death.

Where There’s Pattern, There’s Reason The key thought in the preceding few lines is the article of faith that this pattern cannot merely be a coincidence. A mathematician who finds a pattern of this sort will instinctively ask, “Why? What is the reason behind this order?” Not only will all mathematicians wonder what the reason is, but even more importantly, they will all implicitly believe that whether or not anyone ever finds the reason, there must be a reason for it. Nothing happens “by accident” in the world of mathematics.

Many fields use patterns in various ways: In music and literature, a pattern is the coherent structure or design of a song or book. In art, a pattern is the composition or plan of a work of graphic or plastic art. In architecture, a pattern is an architectural design or style. In psychology, a pattern is a thinking mechanism that is basic to the brain's operation, helping one to perceive things quickly. In archeology, a pattern is a group of phases having several distinguishing and fundamental features in common. In linguistics, a pattern is the manner in which smaller units of language are grouped into larger units...

Every place is given its character by certain patterns of events that keep on happening there.... These patterns of events are locked in with certain geometric patterns in the space. Indeed, each building and each town is ultimately made out of these patterns in the space, and out of nothing else; they [patterns in the space] are the atoms and molecules from which a building or a town is made.

Landscaping is the great cardinal sin of modern architecture. It’s not your garden, it’s not a park—it’s a formless patch of grass, shrubbery and the occasional tree that exists purely to stop the original developer’s plans from looking like a howling concrete wilderness.

God draweth straight lines but we call them crooked.

Nature has introduced great variety into the landscape, but man has displayed a passion for simplifying it. Thus he undoes the built-in checks and balances by which nature holds the species within bounds.

The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight

The impossibility of penetrating the divine pattern of the universe cannot stop us from planning human patterns, even though we are conscious they are not definitive. The analytic language of Wilkins is not the least admirable of such patterns.