While this intriguing tattoo may look like a cross-section of some biological thingummy, it’s actually a visual map of a mathematical formula’s performance. In less huffy terms, it’s a fractal.
- This fractal tattoo creates balance between chaos and order because it was spawned by the coupling of a Julia set and a Sierpinski carpet. [source]
The Julia Set
This fractal tattoo design was created using a Julia set, a mathematical formula that is often used to create complex fractal designs. The Julia set sprang forth from the genius of Gaston Julia, an early 20th century mathematician who initiated a couple of big bangs in the world of mathematics by creating the field of study known as complex dynamics. Although he was all but forgotten for several decades, Gaston Julia’s work was re-discovered by 1980s programmers who were getting creative with their home computers. Using Benoit Mandelbrot‘s Mandelbrot set and Gaston Julia’s Julia set, these early computer boffins created trippy digital art works in the form of detailed fractals. Most of these guys were, after all, born in the 1960s. Computer graphics have now advanced to the point where curious coders can create 3D fractals.
This is an example of a 2D fractal created using the Julia set formula [source]
This 3D rendering of a Julia set fractal resembles a prehistoric sea creature [source]
Chaos Theory
Unlike the Mandelbrot set, the function on the Julia set is “choatic”. Edward Lorenz defined chaos as “when the present determines the future, but the approximate present does not approximately determine the future.” Sounds messy. Well, it’s choas, and messy is what chaos does. What it means for the Julia set is that the future result (the fractal image) that will be produced by the mathematical formula is dependant on how the set starts in the present but there is no way to exactly determine what that future fractal will look like until the equation has been completed. It’s very exciting stuff, and even though I personally didn’t appreciate being subjected to a certain actor for over an hour, the film The Butterfly Effect does neatly describe chaos theory in real world terms. It’s also a good place for aspiring brainers to start.
This double compound pendulum gif shows chaos theory in motion. [source]
The Sierpinski Carpet
Another interesting aspect of this tattoo design is the appearance of Sierpinski holes (the blank spots that give the fractal a lacy appearance). “Sierpinski holes” is the phrase used to describe the gaps in a Sierpinski carpet. Making a Sierpinski carpet is fun. Start with a square and divide it into 9 blocks. Remove the center block. Repeat this process for each block that you’ve just created, and then repeat it for the set of blocks that you’ve just created, ad infinitum. A Sierpinski carpet is considered to be the epitome of order, because you can imagine the finished result before you even get started. Both the process and the result are predictable and so in this particular tattoo the Sierpinski holes symbolize order.
This is a Sierpinski carpet, a predictable design that is created by repeating a specific set of instructions. [source]
Chaos vs Order Fractal Tattoo
By combining a Sierpinski carpet with a Julia set fractal, you get a design that marries order and chaos. This tattoo design is essentially an incredibly complex yin yang because it balances two opposing forces. It’s brilliant, not only in its formation, but in its meaning. This is definitely a tattoo idea for people who like to brain, but remember, someone else already has this fractal as a tattoo. Why not design your own?
More braining on complex dynamics and mathematical sets here, here and here.
