Nature's Patterns: a tapestry in three parts: A review by Live Furustøl

Natures Patterns, a tapestry in three parts

 Philip Ball wrote a book in 1999 called “The Self Made Tapestry; Pattern Formation in Nature”. After realising it was still in high demand, and at a higher price, when it went out of print, Ball decided to rewrite and reorganise the book to be more accessible and made it into a trilogy; Shapes, Flows and Branches. The writings are based on the book “On Growth and Form” by D’Arcy Thompson, first release in 1917, second edition in 1942. Ball is writing about Thompson's findings and filling in his shortcomings with the new discoveries found with new technologies, often through computer simulations. 

Shapes

 The Shape of Things

Shapes and patterns in nature keep repeating themselves. We see the same forms repeated in all different aspects of the natural world; the Amazon River branches itself out like veins in a body, or like a struck of lightning. These similarities used to be presented as a “proof” of God’s intelligent design, but when looking at how these patterns appear, it is clear that they are a product of evolution, of logical and natural organisation. But when it comes to Darwin's theory, the reality is thought to be slightly more complicated. As to how Zebras got their stripes, according to Darwin, the stripes are just what was most effective in survival out of several animals with completely random patterns and that would be presuming zebras have the ability to make all these random patterns. The reality is that zebras, and many other animals, have the ability to make stripes through a complex chemical process in the foetus state, and having stripes happened to be the most effective way to survive. 

Lessons of the Beehive

When looking to nature for structural inspiration, many would look to the beehive. An incredibly precise structure made by an agent-based system. Unlike architects, bees don’t have any grand plan; they only build following a certain set of rules, unaware or maybe indifferent to the greater form. The hexagons are thought to be the optimal shape for maximum honey farming, but the hexagon appears in many other natural phenomena than in hives. If one were to stack soap bubbles in into a bubble raft, they will form themself into hexagons with 120o, just like in hives. If one tries to make hexagons into a dome one quickly realises that something is wrong. A group of chemists faced this problem when working with atoms of graphite and had to contact Buckminster Fuller to inquire about his geodesic domes made a few decades earlier. He presented them Euler’s formula, which claims all hexagon domes, no matter how many hexagons included, needs 12 pentagons to ‘achieve closure’. 

Making Waves

The first and second laws of thermodynamics state that in isolated systems, no energy can be produced or dispersed and the system will increase its entropy, toward thermal equilibrium. A chemical reaction in an isolated system would go from one state towards a final stage. A BZ-reaction is a reaction not following the thermodynamics, which puzzled many chemists when discovered. The reaction is pulsating, changing colours back and forth between red and blue, and when added a catalyst, it forms spiralling patterns and waves. Our planet is not an isolated system; we get a constant increase of energy from the sun and BZ-reactions have been identified throughout nature after its discovery.

Written on the Body

BZ-reactions, reaction-diffusion systems are prominently found in the creation of animal patterns like zebras and leopards. The patterns are actually the same, only dependent on how early in the embryo developmental stage they are defined and the size of the animal. Dotted feline animals often have striped tales. Thin tales often have stripes as the tail is too small to be dotted, while cats with thicker tales, like ocelots, have dotted tales. Once the pigmentation has taken place, it stays. So, if the process happens in an early embryo stage, the pattern will adapt to the size of the embryo and not grow with it. This is how zebras get their stripes. Different species of zebras have a different number of stripes according to how far into the embryo stage it's in, going from around 26 to 55 to almost 80 stripes. 

How Does Your Garden Grow?

Plants, while incredibly diverse, grow in a few sets of mathematical patterns. Most grow in a spiral pattern angled at 137,5o, while the rest of the plants grow in two patterns of 180o. Plants, like sunflowers and cauliflower, have double spiral patterns following Fibonacci numbers. The Fibonacci numbers and the golden ratio is found throughout the growing flora.  

Flow  

Patterns Downstream

Many scientists, physicist and mathematicians have tried to calculate the flow of a downstream river. Most flows of water, turbulent water like rivers and streams, is still too hard to predict, even for supercomputers. But a flow of fluids can also include vortices like whirlpools and hurricanes. Usually, these occur with a circular ‘eye’ but have been observed with other shapes like squares. Saturn has a vortex with a hexagonal structure. The reason for this shape is yet to be understood. 

On a Roll

Hexagons appear again, this time in shallow fluids. If oil is heated in a shallow pan, when the bottom layer is heated and the top layer is cold, the oil will reorganise into hexagonal patterns called convection cells. Convection cells can be found naturally in clouds and as rings and lines in tundras and freezing lakes.

Riddle of the Dunes

Sand is a structural phenomenon. It holds one's weight when walking on it, yet it flows like fluid when poured. Sand dunes, while sand is not a living organism, it is self-organizing. Depending on the grains of sand, the amounts of sand, and the wind, the sand forms dunes in shapes of ripples, crescents and as star dunes. On Mars, where the gravity is lower the dust can form dunes in many other shapes, like drops and horns. Turbulent flow of particles is just as hard to predict as the ones of water, which is why it is hard to predict landslides, as one can’t predict when they will appear, how they will flow and how big they are. 

Follow Your Neighbour

If calling the movement of sand flow, we can also say animals in swarms flow too. The clearest example is schools of fish and flocking of birds. While each animal is a distinct animal, they are part of a larger system; they are agents in an agent-based system. To fly in formation as they do, each bird follows a few set of rules; do not crash into your neighbour, fly in the same direction and speed as your neighbour and steer towards the centre to keep the flock together. The birds, like when bees build their hives, are not concerned with the bigger picture of the flock. It is suggested that when a school of fish are attempted attacked by a predator, the fish only responds to about three neighbours. This can also be applied to people in public areas. Walking down a busy corridor, streams of flow is created, everyone only following the one in front.   

Branches

 A Winter's Tale

The hexagon, or rather the number 6, appears again in snowflakes. While each snowflake is unique, they follow a certain set of rules. They grow out in six directions, and depending on its conditions it will grow plates, columns, dendrites and combinations and variations of those three basic forms. Snowflakes often appear to be symmetrical, but at closer inspection, each arm usually has slight differences in the details caused by minuscule climatic changes from arm to arm. 

Tenuous Monsters

Minerals in stones can branch in dendrite patterns, but unlike the snowflake where each water molecule somehow know where to go, the minerals have no chance of moving and the patterns made is more random. This branching is found in many other things as well; lichens, tumours, bacteria cultures. We can also say that the organisation of people, in cities, branches itself like this. Experiments have been made comparing bacterial growth to the growth of cities. If the environment of bacterial growth is made to mimic the geographical conditions and settings of a city, the bacteria will grow remarkably similar to said city.

Just for the Crack

Cracking is another form of branching. Often thought of as the form of a lightning strike but can appear in many other ways. The shape of the crack in a glass is determined by the speed. A slow crack will produce a straight line. With an increased speed, the crack will first form perfect waves and at high speed, it will be unregular and appear random. Not all cracks start from one point; if a thin surface dries out, the crack happens everywhere at the same time. This is found in dried mud and on old paintings. If after more drying, each ‘island’ in the cracked system will repeat the cracking process and split into even smaller pieces. Once again, we can relate it to the urban sprawl; how cities are ‘cracked’ in several scales. These types of cracks can also appear in highly regular forms, again the hexagon, as seen in The Giants Causeway in Northern Ireland.

Water Ways

Rivers is another branching phenomenon. They are slowly formed by erosion through the landscape. The rivers can branch is several arms, and each arm can branch in several arms and so on, creating a fracture: a pattern repeating itself in many scales. Looking at an aerial picture of a fractally branched river it can be hard to tell whether you’re looking at one or one thousand miles of river. The rivers are thought to branch out to disperse the energy of the water evenly, to keep the flow of water as low as possible. In a straight stream, where all water will naturally go the same direction, the water will still branch out but come back again, creating a braiding of streams. This erosion will over time cause a series of hills or bumps. This can also be found in areas of ice, where braided flows of melted water create inverted icicles. 

Tree and Leaf

When trees grow, it needs to find a balance between being tall and big enough to gain enough sunlight, while still being sustained by the branches. Leonardo Da Vinci observed a few rules as to how trees and plants branch out by predicting the angles in which they grow. These rules were later simplified into three points; 1- if a branch splits into two equal parts, the parts will be equally angled, 2- a smaller split branch will grow at a higher angle than the thicker branch and 3- if one branch splits so small that it does not disturb the main branch, it will branch outwards of and angle between 70o and 90o. These rules were written for arteries, but they’ve found them to apply to plants as well. 

Web Worlds

 As people, we organize ourselves in social networks. We have friends that know our colleagues that know our cousins that know our dentists etc. Living in a city, or a community, we daily create a network of interaction. Therefore, disease outbreaks, like Covid-19 are so dangerous. It is hard to get the full extent of the network of an infected person, and how far the disease has spread. 

The Threads of the Tapestry

“Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry” (Feynman, 1965). Philip Ball wraps his books up with this quote. Patters keep repeating themselves in all parts of nature, and more often than we would think, we humans unconsciously produce the same patterns too.