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BLOCK BLAZER

**Chaos Theory.**

Chaos is the science of surprises, of the nonlinear and the unpredictable. It teaches us to expect the unexpected. While most traditional science deals with supposedly predictable phenomena like gravity, electricity, or chemical reactions, Chaos Theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on. These phenomena are often described by Fractal Mathematics, which captures the Infinite Complexity of Nature. Many natural objects exhibit Fractal Properties, including landscapes, clouds, trees, organs, rivers etc, and many of the systems in which we live exhibit Complex, Chaotic behavior. Recognizing the Chaotic, Fractal Nature of our world can give us new insight, power, and wisdom. **Principles of Chaos**

**Koch Snowflake: Finite area, Infinite perimeter.**

The Koch Snowflake has finite area but infinite perimeter… yeah that happens with fractals. This abstract curve requires an infinite process (depicted in the gif) to construct and is an example of a* fractal*–a mathematical set (usually a curve or geometric figure) which exhibits a repeating pattern that displays at every scale. (More about fractals here https://en.wikipedia.org/wiki/Fractal)

*But How?* It seems clear that the area would be finite since the figure encloses a finite amount of space. To grasp why the Koch Snowflake has infinite perimeter, notice how as the iterations progress, the edges become more and more intricate. Now imagine trying to draw the edges with a pen. Since the construction of the snowflake continues indefinitely, the edges become infinitely intricate and you could never finish detailing these intricacies with your pen (that is the intuitive argument at least. I’ll leave the precise calculations up to you).

Fractals may seem so abstract and impractical but they actually have many useful real-world applications. For example, Benoit Mandelbrot (considered the “father of fractals”) found that stock market prices could be modeled with a factual curve. Check the wiki page for a long and diverse list of applications.

Fractal geometry may seem more abstract than traditional geometry but Mandelbrot argues that fractals are **“the geometry of nature”**. Objects in nature have random irregularities and are seemingly infinite in their intricacies. Attempting to incorporate this in drawings or animations is extremely difficult. Movie special effects and CGI often use fractals to make objects appear more natural looking. Since fractals can be made with mathematical formulae they are easy to generate with a computer. The first *Star Wars* movies were renowned for their special effects and were some of the first to use fractals to generate life-like explosions and landscapes of other worlds.

More at https://Instagram.com/zouassi

The hidden dragon.

Based on the dragon curve.

The Golden Ratio and Secret Geometry in Nature

“*These wonderfully symmetrical plants show the fractal nature of math, physics and the universe. Could this be evidence of sacred geometry? “Look deep into nature, and then you will understand everything better.*”
-Albert Einstein

The Golden Ratio, or Fibonacci sequence, is everywhere. It can be found in ancient architecture, in some of the world’s most beloved artwork (such as the Mona Lisa), and most definitely in nature. It’s for this reason that the intriguing sequence, which begins as 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on forever, has fascinated mathematicians, scientists, designers, and artists for centuries.

Leonardo DaVinci, for instance, was known to use the Fibonacci sequence in his masterpieces because the pattern is aesthetically pleasing. Is it a coincidence that the ratio can be seen from a micro to macro scale in all biological systems, and even in inanimate objects? Clearly, there’s much to learn about sacred geometry and inherent order in the universe.

Some theorize that the phi ratio (phi = 1.61803…) is evidence that nature is inherently perfect, and that when mankind strays away from the natural law, sickness and imbalance occur. While the Golden Ratio doesn’t account for every structure or pattern in this world and others, it most certainly is a key player.

Beautiful, damn hard, increasingly unuseful. That’s fractals.

—
Benoît Mandelbrot

Infinite Growth

Experimental Psychedelic: Tree of Life 2

This is one of the first images I made with Processing.

A Julia Set is a set of complex numbers generated using a recursive relationship. I created one last semester in MATLAB for a math assignment and thought I’d share some cool screenshots.

I tried to increase the resolution but my computer crashed :(

anonymous asked:

What is Benoit B. Mandelbrot's middle name? Benoit B. Mandelbrot

Experimental Psychedelic: Tree of Life 5

Dan Winter - Eartheart