THE PROJECT

Recall that the Mandelbrot is the set of points $c$ of the complex plane such that iterating the function $f(x) = x^2 + c$ starting from $x=0$ does not diverge to infinity.

The Julia set corresponding to a point $c$ of the Mandelbrot is defined as the set of points $z$ such that iterating the function f starting from $x=z$ does not explode to infinity.

Hence, by definition, to each point $c$ of the parameter space where the Mandelbrot sits, there corresponds a unique Julia set in the dynamical space.

The relationship between these two fractals is intimate and deep. In particular, points inside the Mandelbrot correspond to connected Julias, while points outside of it give rise to disconnected Julias.

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.

Examples
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
30% 1
20% 2
20% 3
30% 4
4
SHRINKAGES
33% 100 bps
33% 10 bps
33% 1 bps
3
WHAT IS A JULIA 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 Julia Set is one of the most well-known fractal set derived from the works of Gaston Julia in the 20th century.

As part of the Fractal Dimensions project, 4’200 Julias art pieces representing the Julia Set were created. Those art pieces were designed for entertainment-purposes only and shall not be considered as financial investments.
HOW WILL THE MINTING PROCESS WORK?
The presale will start on Friday, September 17th at 10am PST/7pm CET and will last for 48 hours. During this time period, Mandelbrot holders (1 Julia per Mandelbrot) and Free Mint Julia (FMJ) token holders (1 Julia per token) will be able to claim their free mint, while holders of VIP tokens (VIP) will be able to pre-mint a Julia at the normal rate (0.1978 Ξ). After the 48 hours period (approximately on Sunday September 19th, at 10am PST/7pm CET, the sale will open to the public until all remaining Julias have been sold.
HOW TO CLAIM MY FREE MINT?
1) If you are a Mandelbrot owner you will have the possibility to request a free mint (Gas only) for each Mandelbrot you own starting on Friday September 17th at 10am PST/7pm CET and during a 48-hours period.
2) If you own a Free Mint Julia (FMJ) pass, you will also have the possibility to request a free mint (Gas only) during the exclusivity period.
You will be able to claim from our website or directly from the contract on etherscan.
WHAT'S A VIP TOKEN?
With the vip token (VIP) you can buy a Julia at the normal rate (0.1978 Ξ) during the 48-hours exclusivity period.
You will be able to use it from our website or directly from the contract on etherscan.
HOW CAN I GET A VIP TOKEN?
HOW MUCH DOES A JULIA COST?
A Julia costs 0.1978 Ξ. You are allowed to buy a maximum of 20 pieces per transaction. Minting closes when all 4200 pieces have been minted. There is no time limit to mint.
WHY ARE THERE 4200 TOKENS?
For each Mandelbrot of the first collection (1978 pieces), there exists two Julias point that are mathematically linked to their original Mandelbrot. Hence, the total supply of Julias will be of 4200 pieces. As we are using a dedicated contract for the new collection, both collections will be independent on OpenSea. In addition, several lucky minters will be awarded a limited edition piece from the following editions (no actions needed, the limited edition pieces will be randomly airdropped during the minting process):
- 50 images from our guest artist Maths Town
- 66 videos from our guest artist Maths Town
- 128 videos from our artist Abramo
HOW DO I BUY A JULIA?
You can buy from our purchase page or directly from etherscan using the contract purchase function. When the collection is sold out, you can purchase a Julia directly on Opensea.
Are any funds used for charity?
5% of the revenues will be donated to charity. Social impact is one of the key pillar of our project, and we will be honoured to support the exceptional people dedicating their lives to others. You can see some examples of the associations to which we have donated in the past on our Twitter account.