There are patterns in the natural environment that result from physical and/or biological processes. Looking into these patterns, understanding their structure, and applying them to a function is a powerful way to solve complex, dynamic problems. So what patterns do we see in the natural environment?

One of the most basic patterns found in nature is circles. Almost all natural systems appear to occur within cyclical patterns, like the movement of the Milky Way Galaxy, the Earth’s orbit around the Sun, seasons, molecular recycling like the rock cycle, the water cycle, the carbon cycle, the nitrogen cycle, the phosphorus cycle, and the life cycle.

Most industrial models of first world nations are linear, that is, there is an input (resources) and an output (waste). Sustainable models, on the other hand, are (would be) cyclical. That is, there is an input (resources) and an output (waste) that then serves as the next input (resources). This is what is known as a “closed-loop system”. In mathematics, functions that operate this way are called “iterative processes”.

The Recycling logo - a common symbol of a closed-loop industrial model.

This short video, Doodling in Math, is a fun introduction to more patterns that can be observed in nature. There is a Part 2 and Part 3 if you are so intrigued, plus many other related videos in YouTube land.

What those videos are getting at, in a nutshell, is a number of emerging, related fields we are now beginning to understand, including dynamical systems, fractal geometry, chaos and complexity. Here are some concepts which these fields build upon:

The Fibonacci Sequence = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.

This sequence is obtained through an iterative process. The mathematical steps are shown in the first video. (0+1=1, 1+1=2, 2+1=3, etc.) Any iterate (n) of the sequence can be calculated with the equation x(n)= x(n-1) + x(n-2). The more times you iterate the function, the ratio x(n-1)/x(n-2) approaches the number ‘phi’ (1.61803399…). This has historically been called The Golden Ratio, and was used in everything from Roman architecture to Renaissance art, from ancient African civilizations to modern metal songs like Tool’s Lateralus.

Another way to visualize phi.

The Mandelbrot Set.

These distinct patterns are called ‘fractals’ and although many had hinted to their existence throughout history, (as far back as Leonardo di Vinci, who noted the mathematical pattern of trees) we have only begun to truly understand the depths of these patterns. Our recent advantage comes from the computing power of modern technology that has allowed us to iterate functions millions of times (which would be very, very tedious work by hand). Many people have contributed to our understanding, including Pierre Fatou, Gaston Julia, Stephen Smale, and James Yorke. It was only in the 1980s, after computer technology at IBM was taking off, did mathematician and physicist Benoit Mandelbrot discover the complexity within fractal geometry. All of the necessary and sufficient conditions of something being a fractal is yet to be determined, but fractal properties include self-similarity (zooming in on any range of scale reveals a statistically similar pattern), a non-integer dimension (possessing geometry between 2 and 3 dimensions, as opposed to Euclidean geometry), and complexity (described by “D” that is derived from the slope of a double log plot). Since then, we have used this knowledge to explain how long the coastlines of continents are, how subatomic particles behave, how a forest is structured, how galaxies cluster, how weather forms, how mammalian brains fold as they grow, how plants maximize solar access, how erosion shapes the landscape, how populations change through time, how plate tectonics change through time, how fluid behaves in a dynamic system, how action potentials in neurons transmit signals, how roots grow, how to reposition satellites in orbit around the Earth, even how to model DNA, the structure of life itself. Fractals, then, have the ability to not only describe the structures in the natural world, but also model the processes by which they function. This is a very useful tool, indeed.

So, it is with this level of knowledge about the natural world that we step into realm much less quantitative, that of philosophy. In my next post I’ll describe some different worldviews, their relative merits, and introduce permaculture.