One of the characteristics of evolution is the presence of harmony. In the fractal theory evolution and genomes seemed to have different ends. However, Nature self expression comes in rich forms, physical structures and empty spaces that are not empty. The most common pattern observed in nature was studied in sequence of numbers known as Fibonacci ¹ numbers. This is a sequence in which each element is the sum of the two elements that precede it. We can find the Fibonacci numbers often in mathematics as well as other science areas. The application of the sequence was first documented in India 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. Today it is used for computer algorithms, data structures. In graph theory, the Fibonacci cubes or Fibonacci networks for interconnecting parallel and distributed systems. In biological settings we can find it as branching in trees, the arrangement of leaves on a stem, the flowering of an agave, the most common shared image is the arrangement of a pine cone’s bracts or the nautilus shell.
In mathematics, The word fractal is defined as a geometric shape containing detailed structure at arbitrarily small scales. In other words, smaller and smaller copies of a pattern are successively nested inside each other, so that the same intricate shapes appear no matter how much you zoom in to the whole. Mandelbrot², known as the father of “fractalist” is recognized for his contribution to the field of fractal geometry, which included coining the word “fractal” in 1975, as well as developing a theory of “roughness and self-similarity” in nature. The term “fractal” as it is derived from the Latin word “fractus”, defined as broken or shattered glass. Fractals are also found in human pursuits, such as music, painting, architecture, and in the financial field. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry.
Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
—Mandelbrot, in his introduction to The Fractal Geometry of Nature
“So the goal of science is starting with a mess, and explaining it with a simple formula, a kind of dream of science.”
Fractal Dualities On Exhibit July 4 – Sep 4 2005
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Before 7:00pm use Parking kitty app about $2.70 per hour.
Parking lots around the District 4 available.
The nautilus is a marine mollusk considered a “living fossil”. Often related as a living example of the sequence, it is one of the oldest organisms on the planet still alive today. This self-similar spiral is observed in molecular structures to animal behaviors to galaxy formations. As far as we know this is the most efficient way for something to grow. By maintaining the same shape through each successive turn of the spiral, the least amount of energy is used; like a sphere. Fractal dualities it’s just a reminder of life’s wonders and our humble voyage navigating cycles of existence under a time concept that may or may not exist in the same way that is perceived in our planet. The photography series honor the agavaceae plants deconstructed in monochromatic representations on their relationships with their environment.
(1) Leonardo Bonacci was an Italian mathematician considered to be “the most talented Western mathematician of the Middle Ages” commonly known as Fibonacci.
(2) Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as “the art of roughness” of physical phenomena and “the uncontrolled element in life”. He referred to himself as a “fractalist” and is recognized for his contribution to the field of fractal geometry, which included coining the word “fractal”, as well as developing a theory of “roughness and self-similarity” in nature.
