Quotes About Patterns

Research employing fractal rules has revealed a three-quarter power law even in the circulatory system.

Self-similarity on all scales is a key factor in understanding and describing nature's phenomena.

Real-world images have redundant information. Tree bark has repeating patterns with small variations.

Zooming into the boundary of the M-set, we find smaller and smaller island molecules, surrounded by increasingly intricate circular patterns, evocative of Oriental art, particularly in the meditative designs of Buddhism known as mandalas.

Nature finds the same solution to many different problems, like how to drain water from the land into the oceans, and how to get blood from our hearts to our fingertips and back again. And the templates that nature uses are fractals. Clouds look the same at all scales. It is impossible to determine the size of a cloud from a photograph of it.

Dimensional Magic We are fractal. Our lungs, our circulatory system, our brains are like trees. They are fractal structures. Fractal geometry allows bounded curves of infinite length, and closed surfaces with an infinite area. It even allows curves with positive volume, and arbitrarily large groups of shapes with exactly the same boundary. This is exactly how our lungs manage to maximize their surface area.

Art is about those things which we do not always immediately recognize or understand. The artist helps us to see things more clearly, revealing previously hidden patterns to us. Art is fractal. Art reflects and expresses the fractal nature of our conscious perceptions of the world, as interpreted by our fractal brains.

The signature of chaos is the fractal attractor-fractals are the patterns of chaos

Period-doubling is a general principle of nature.

Afformations are empowering questions that immediately change your subconscious thought patterns from negative to positive.

When such patterns are triggered in therapy, it gives the patient a chance to look at them and change them, for as we saw in chapter 4, "Acquiring Tastes and Loves," positive bonds appear to facilitate neuroplastic change by triggering unlearning and dissolving existing neuronal networks, so the patient can alter his existing intentions.

The patterns of a century ago may be a harbinger of what we are facing now. In many ways, the megathreats of today are worse than the threats of a century ago.

I was heartbroken, but used to it; the patterns of struggle and failure in life tend to repeat themselves.

And the quiet of the house is also the quiet of stalks and vines that no longer jangle at any touch of of wind, or bird, or person passing, but which have been laced and bound into new patterns and have been now given new stories to tell. Stories that lace and bind the earthly matters to matters not of earth.

Chatter requires a very finely-tuned sense of empathy, conversational techniques, and cultivating a presence – it's not about just going down a checklist of topics. It also requires reading between the lines of what people say, examining body language, and noting patterns of human interaction to different types of stimuli.

People see stories everywhere," Regine says. "That's what my father used to say. We take random events and we put them together in a pattern so we can comfort ourselves with a story, no matter how much it obviously isn't true." She glances back at Seth. "We have to lie to ourselves to live. Otherwise, we'd go crazy.

People see stories everywhere...That's what my father used to say. We take random events and we put them together in a pattern so we can comfort ourselves with a story, no matter how much it obviously isn't true.

People see stories everywhere," Regine says. "That's what my father used to say. We take random events and we put them together in a pattern so we can comfort ourselves with a story, no matter how much it obviously isn't true." She glances back at Seth. "We

language is learned through our perceptual and cognitive experiences and that like all other aspects of learning, language learning involves the discovery, categorization, and determination of patterns through the use of language.

I stared up at the plaster ceiling as I had done as a child. It seemed to me that the vibrating patterns overhead were sliding into place. The mandala of my life.

handicapping heaven, searching for patterns, and a portal of probability opening up onto the meaning of life

From all this rapid-fire activity—five trillion chemical processes a second—we form patterns of meaning about the world.

In our analysis of complex systems (like the brain and language) we must avoid the trap of trying to find master keys. Because of the mechanisms by which complex systems structure themselves, single principles provide inadequate descriptions. We should rather be sensitive to complex and self-organizing interactions and appreciate the play of patterns that perpetually transforms the system itself as well as the environment in which it operates.

the product of two sums of two squares of integers is always expressible, in two different ways, as the sum of two squares of integers.