Monday, March 23, 2015

Patterns in Nature - Scott Werner - Research Project

Plato: (looking at only his work on Natural Patterns) argued for the existence of universals, Considered ideal forms
Leonardo Fibonacci: Fibonacci Sequence
Joseph Plateau: Minimal Surface with given boundries
Adolf Zeising: Golden Ratio
Wilson Bently: took first micrograph of a snowflake
Alan Turing: Known for computing and codebreaking wrote “The Chemical Basis of Morphogenesis” Predicted Oscillating Chemical reactions such as “Belousou-Zhabotinsky reaction” how stripes or spots are determined
Aristid Lindenmayer: Developed L-system, formal grammar to model plant growth patterns in the style of fractals

The Belousov-Zhabotinsky reaction is a faimly of oscillating chemical reactions. During these reactions, trasition-metal ions catalyze oidation of various, usually organic, reductants by bromic acid in acidic water solution
Belousov has discovered the first reaction of this class with the Ce3+/Ce4+ couple as catalyst and citric acid as reductant. He observed that the color of the reaction solution oscillated between colorless and yellow and found that the frequency of oscillations increased with rise of temperature (Belousov, 1959; 1985). Zhabotinsky replaced citric acid with malonic acid (MA) to create the most widely used version of the BZ reaction (Zhabotinsky, 1964a). He has shown that the oscillations in the solution color were due to oscillations in concentration of Ce4+ (Fig. 1). He further found that oxidation of Ce3+ by HBrO3 was an autocatalytic reaction and self-sustained oscillations of Ce4+ concentration arose after accumulation of bromomalonic acid (BMA). He demonstrated that Br- ion was an inhibitor of the autocatalytic oxidation of Ce3+. He suggested that the BZ reaction consisted of two main parts: the autocatalytic oxidation of Ce3+ by HBrO3 and the reduction of Ce4+ by MA and its bromoderivatives, which were produced during the overall reaction. In his scheme, the Ce4+ reduction is accompanied by the production of Br- from the bromoderivatives of MA. Br- is a strong inhibitor of the autocatalytic oxidation of Ce3+ because of its rapid reaction with the autocatalyst, which is presumably HBrO2 (Zhabotinsky, 1964a,b).

The fibonacci Sequence fits perfectly within the golden ratio, this concept has been used to check against some of considered best artwork done in the world and throughout time
The Fibonacci numbers are Nature's numbering system. They appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple. The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even all of mankind.
Plants do not know about this sequence - they just grow in the most efficient ways. Many plants show the Fibonacci numbers in the arrangement of the leaves around the stem. Some pine cones and fir cones also show the numbers, as do daisies and sunflowers. Sunflowers can contain the number 89, or even 144. Many other plants, such as succulents, also show the numbers. Some coniferous trees show these numbers in the bumps on their trunks. And palm trees show the numbers in the rings on their trunks.

A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract fractals – such as the Mandelbrot Set – can be generated by a computer calculating a simple equation over and over.

A book that discusses how mathematics and harmonics affect our brain and perceptions but also suggests that it can be applied to nature.

Using underwater cameras the team discovered the artist is a small puffer fish only a few inches in length that swims tirelessly through the day and night to create these vast organic sculptures using the gesture of a single fin. Through careful observation the team found the circles serve a variety of crucial ecological functions, the most important of which is to attract mates. Apparently the female fish are attracted to the hills and valleys within the sand and traverse them carefully to discover the male fish where the pair eventually lay eggs at the circle’s center, the grooves later acting as a natural buffer to ocean currents that protect the delicate offspring. Scientists also learned that the more ridges contained within the sculpture resulted in a much greater likelihood of the fish pairing.

The size of the columns, which varies from site to site between a few inches and a few yards, is primarily determined by the speed at which lava from a volcanic eruption cools," says U of T physics professor Stephen Morris, who supervised the thesis project of PhD student Lucas Goehring. Cooling lava sometimes forms strange column-shaped formations with a remarkable degree of order. The most famous of these hexagonal columns are found at the Giant's Causeway in Northern Ireland, where they are said to be the work of Finn MacCool, an Irish giant.


Thanks and Enjoy!

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