THE PROJECT

Fractals are self-similar objects, that is, they appear the same at different scales. First theorized in the 17th century by the mathematician and philosopher Gottfried Leibniz, fractal shapes are common in the empirical world, with examples including plants, coastlines, human blood vessels and pulmonary vessels, DNA, and ocean waves.

The Mandelbrot Set is the most popular, the most studied, and the most fascinating mathematical fractal discovered by humanity. This gift of Natures takes its name from the mathematician Benoit Mandelbrot, notorious for his monumental contribution to the field of fractal geometry. A subset of the Complex plane defined by the properties of the simple polynomial $z^2 + c$, it contains an infinite amount of astonishingly beautiful and incredibly complex patterns.

Examples

Even though exploring the totality of its richness is impossible for finite beings, we are fortunate enough to live in the age of information. Modern computers allow us to numerically approximate the boundaries of the Mandelbrot set up to a certain level of depth. However, the magic world hidden in the Mandelbrot becomes more complex and more interesting as one increases the zoom factor. As our civilization advances and more powerful computing machines will become available, future generations will have the luxury of enjoying the deeper and deeper wonders of the Mandelbrot.

Mathematically, the Mandelbrot is defined as the set of points $c$ of the complex plane for which the function $f(z) = z^2 + c$ does not diverge to infinity when iterated from $z=0$. Here $c$ and $z = a + b\,i$ are complex numbers with real and imaginary components, and $z^2 = a^2 - b^2 + 2ab\,i$ denotes the complex product of $z$ with itself.

The Mandelbrot Set Collection is a curated selection of points from the Mandelbrot, generated with a numerical algorithm and engraved into 1978 unique NFTs. Each work represents the neighborhood of one of our favorite points of the fractal, with a random zoom factor and colored with arbitrary gradients based on the number of iterations of $f$ before the point diverges to infinity.

Not all the attributes are equally likely, thus giving rise to different degrees of scarcity for each artwork. In particular, higher zoom levels are limited and golden-colored points are very scarce. Attribution is random, so we wish you the best of luck in unveiling one of the most out-of-the-ordinary pieces.

Attributes
POINTS
20% Attractor
15% Helix
15% Fabric
10% Dragon
10% Virus
10% Snake
10% Flux
5% Coral
5% Manifold
9
LOCATIONS
30% Surface
25% Shallow
20% Profound
15% Deep
8% Deeper
2% Abyss
6
COLORS
2% Gold
7% Space
7% Fashion
7% Jamaica
7% Summer
7% Ice
7% Rainbow
7% Lava
7% Sky
7% Lake
7% Ocean
7% Kiwi
7% Sunset
7% Sunburst
7% Mint
15
CYCLES
50% 1
25% 2
15% 3
10% 4
4
SHRINKAGES
33% 100 bps
33% 10 bps
33% 1 bps
3
WHAT IS A MANDELBROT FRACTAL?
A fractal is a never-ending pattern integrating infinitely complex shapes that are self-similar across different scales. They are created by repeating a simple process in an ongoing feedback loop. The Mandelbrot Set is one of the most well-known fractal set derived from the works of Benoit Mandelbrot in the 20th century.

As part of the Fractal Dimensions project, 1’978 Mandelbrots art pieces representing the Mandelbrot Set were created. Those art pieces were designed for entertainment-purposes only and shall not be considered as financial investments.
How much does a Mandelbrot NFT cost?
A Mandelbrot costs 0.1978 Ξ. You are allowed to buy a maximum of 5 pieces per transaction. Minting closes when all 1'978 pieces have been minted. There is no time limit to mint.
Why are there 1978 tokens?
This fractal was first defined and drawn in 1978 by Robert W. Brooks and Peter Matelski as part of a study of Kleinian groups. On 1 March 1980, at IBM's Thomas J. Watson Research Center in Yorktown Heights, New York, Benoit Mandelbrot first saw a visualization of the set.
How do I buy a mandelbrot NFT?
You can buy from our purchase page or directly from etherscan using the contract purchase function
Will mandelbrot NFT have utility?
We reserve 10% of the earnings for the community, which will be used for future events like raffles, airdrops and.
Last but not least, all Mandelbrot owners will have exclusive benefits for upcoming collections.
Are any funds used for charity?
5% of the revenues are used in charitable operations, we believe that education is a fundamental resource