What is Collection #3?
Hello readers,
It’s with great excitement that I am announcing and releasing the third collection in the atlasautomata art project. This set of plots reflects a slightly deeper aspect of my personal interests, as it relates to mathematical exploration I’ve been conducting gradually for the last four years or so. I’ve never previously written about this mathematical work, and have only shared the full extent of it in-depth with a handful of people.
In short, the eight pieces in 'Collection #3' represent different sets of nested views of just one interesting example out of the numerous mathematical objects I have encountered over the course of this study. I’ll explain a little more about the underlying mathematics of the structure in the next section of the post. But first I’ll explain some of the physical details and aesthetic choices of this set of plots…
All of these plots are 9” by 12” in size, and printed on 2-ply Bristol Paper - you need a tough piece of paper when the pen crosses over the same point over one-hundred times in some cases! The first four plots of the collection are comprised of three superimposed sets of 36 loops of the underlying structure, with a slight angular shift on the perspective each loop, and each set being a different colour to create a naturally emerging chromatic effect. This a total of 108 loops, reflected in the $108 asking price, and also in the total area of the paper (9 x 12 = 108).
The second half of the collection mirrors (literally) the first half, but uses 34 shifting loops of the mathematical structure per colour set instead of 36. This totals 102 loops, reflected in the pricing, but the size remains the same. The reason I did this was to reveal how sensitive the emergent chromatic effect is; each plot looks quite different to its mirrored counterpart as a result. Also, 34 is a Fibonacci number, which forms a new resonance with the structure itself, which I like to think makes up for the sizing not shifting to reflect the different number of loops. Each plot comes out slightly differently due to this chromatic sensitivity… Even if I re-printed the entire collection, the results would be unlikely to match exactly due to natural variations in the alignment of each layer, pen pressure, and other subtle factors!
[Note: I decided not to include any text on the plots this time, as I think these structures are best represented without identity or narrative inflation - as pure mathematical objects available for anyone to discover. However, there will still be a certificate of authenticity on the back, and in the bottom corners, I will number and ‘mark’ each plot in very, very small writing (which isn’t reflected in the scans)]
(Framed example - [1 of 8] used for demonstration purposes)
“So what actually is it though?”
Without revealing absolutely everything that goes into it - essentially the underlying structure is an example of a seemingly unlikely ‘closed path’ I have found when exploring the Fibonacci numbers under modular analysis in geometric ways.
“Okay, what does that mean?”
The Fibonacci sequence is a series of numbers whose next member is always the sum of the previous two (starting with 0 and 1). 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… and so on forever. The ratio between these numbers as they get bigger converges on the extremely popular ‘Golden Ratio’ which is used in all kinds of aesthetic creations. Modular analysis of this sequence is essentially the process of dividing all these numbers by some set number you’re interested in, and looking at the remainders or ‘residues’. When you do this for the Fibonacci numbers with any set number, you get a repeating cycle of these residues. This plot is directly informed by the Fibonacci sequence under this kind of modular analysis, with the set divisor in this case being 305.
“How does this cycle of remainders become this structure?”
After a lot of exploring, I found a way to represent these cycles as vectors in 3D spaces, under a simple fixed turning algorithm. I used Python to convert 10,000’s of these modular residue cycles into geometric paths in 3D space, and to my great surprise and delight, some of them formed ‘perfect closed loops’ starting and ending at the origin point in the 3D space. This structure is reflective of one such example of a closed loop, but rendered into ‘artwork’ via aesthetic choices.
I’ve been researching and refining this phenomenon, and others related to it ever since I encountered it a few years ago. This mathematical process is only the tip of the iceberg, but I am excited to take the small step of putting these structures out there into the world. Thank you for your interest in this project, and if you do make a purchase - thank you from the bottom of my heart. I hope you enjoy these plots!
- Richard Ferreday (Atlasautomata)