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Fractal Friends

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. Geometrically, they exist in forms and shapes that are very familiar to us. Nature is full of fractals. For instance: trees, ferns, river networks, coastlines, mountains, clouds, hurricanes, seashells, broccoli, or cauliflower.

 

Mathematical fractals – such as the Mandelbrot Set – can be generated by a computer calculating a simple equation repetitively, feeding the answer back in to the start. These fractals are infinitely complex, meaning we can zoom in forever if we were sufficiently equipped with computational power.

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Self-similarity of Fractals

Benoit Mandelbrot, a polymath, developed the branch of fractal geometry. This geometry recognizes a hidden order in the seemingly disordered, regular patterns in the roughness of nature. A fractal can be understood as a rough shape that can be split into parts, each of which is then a close approximation of its original-self. This character of self-similarity means that shapes of seemingly great complexity can be constructed by a simple rule of iterations on a computer thereby mimicking nature. 

Would you like to see for yourself and go deep down the fractal rabbit hole? Then play this video (did you manage to watch the full ten minutes?):

Fractals and the Power Law

There is a close relationship between fractals and the power law. As a matter of fact, the power law itself is self-similar. To illustrate this, let's take a look at financial markets. More specifically, when it comes to asset prices and fractals, think of hourly, daily, weekly, monthly or yearly stock price moves. Remove the x-axis labeled 'time', and they all look pretty much alike. 

Furthermore, markets, like oceans, have turbulence. Mandelbrot observed that the underlying power law that is evident in random patterns in nature also applies to the positive and negative price movements of many financial instruments. On most of the days, the change in markets is small and things are quiet, but on a few days markets gyrate wildly. Only fractals can explain this kind of random change. 

While Mandelbrot's theory won't help us predict where a stock, commodity or token price is going or help us value a project, it can help us extract and understand the nature of the randomness of markets. Taking the insights from the power law to heart, extreme changes in asset prices are much greater than you would expect from other more conventional probability models, but it is in extreme events where ruin - and massive gain - is found. Fractals can therefore help us better understand and recognize risk - a prerequisite for successful investing. 

The Collection

Each single Fractal Friend is uniquely determined by a combination of the resolution size of the Mandelbrot set, the color combinations for coloring the picture inside and outside of the set, and the coloring patterns.

  • The resolution is like the boundary precision of the Fractal Friend. Increasing this value will create more accurate calculations and images with finer contours, while also increase processing time.

  • The coloring patterns that surround each Fractal Friend is governed by the so-called potential. This is a concept from physics which describes a field in space, from which many important physical properties are derived, like the gravitational, electric or thermodynamic potential.

We parametrized each of the three defining dimensions with a preset range of values which would have amounted to 339,796,892,160 possible images. Out of these 339,796,892,160 possibilities, we randomly selected 10,000 realizations and then hand-picked 2,001 final ones in a curation. Some images, particularly the simpler ones in the collection, were generated with intention.

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Airdrop
Closes on Sep 10th 2021 @ 11:00am EST
 

How to participate?

  • Follow@theIntuitiveQ on Twitter

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Lottery rules:

  • After the close, winners will be determined randomly

  • A participant can only win one Fractal Friend

  • Every participant has an equal chance of winning a Fractal Friend

  • Only participants who signed up before the 9/10 11am EST close will be considered (it's timestamped)

  • The winners will be notified via Twitter Message

  • Winners can pick the Fractal Friend priced at 0.25 ETH they like

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