Ordinal Stream

Although I had a background related to basic sciences by studying chemistry in a polytechnic school, I had a hard time with pure mathematics while I could easily apply them to other sciences and concepts. My level was actually so bad that in 2013 I was deciding to take an IQ test to understand what were my weaknesses and strengths. I eventually ended up with better results in language concepts than in mathematics and I was struck by this reality so bad that I left sciences to attend to an art school in Media Interaction Design; a new field in between computer programming, motion design and graphic design and the whole experience changed my life. I already knew I had some skills in programming while I had to build entire chemical simulation using code during my chemistry studies but I had no idea that mathematics, computer sciences and language were so deeply interconnected so that studying these sciences was actually easier knowing that I had better skills in language and expression. Today this reality appears logical as mathematics are simply manipulating axiomes in order to describe numeric transformations that apply to the laws of models so strong that they shape technology and society. Creating a computer algorithm is then formulating a theory which can be proven by applying a set of rules based on logic and it appears that such abilities are requiring to use different functional parts of the brain and are not entirely depending on the ability to do mathematics or apply logic but more to the idea that we mostly think with words before making concepts even of the most technical subjects. Maths are just a code to apply what we call intelligence in the meaning of « read between the lines » or in a more abstract way bending information while encapsulating ideas into concepts to express them and even apply them to theories and sciences. It’s a long road that led to these ideas as I became aware that all sort of mathematics were actually understandable when I was applying them to computer science or chemistry and they are a major actor in proving facts as they answer to kind of a single logic that seem to apply beyond our simple observations as universal laws.

I had attended to several classes of calculus, trigonometry or linear algebra without giving any sense of these fields beyond their application to physics and as I was rushing into an experimental generative art projects it took me a month to understand completely the maths I needed to use to build the simulation of a tensor field from which I had the idea to create abstract visuals in digital art made with code. A tensor is a mathematical object like a vector with multiple dimensions and that can be describe with matrix while a tensor field is a mathematical object that can be described as a mapping of multiple matrix in the space. Luckily when applied to computer sciences and code these concepts were more understandable and the idea was to put a particle without any information of mass at a random spot on a vector field and let the particle draw trajectories depending on each vector components of the field acting on the particle like forces and making it move in a controlled randomness. They were plenty examples of these simulations across the web and it gave me a good base to start building the tensor field. It’s while making some research on the web that I became aware that these models were actually a way to solve numerically differential equations and with the help of scientific publications in computer model I begun to understand the maths related to the project. The idea was indeed to integrate the position of a particle which forces that apply regarding the tensor components describing velocity and acceleration at every points in a defined space (the screen of a computer). I was remembering my physics courses and it became clear how I could apply those maths to the project as acceleration and speed could be derived from the position of a particle. It’s with the help of online publication that I found the mathematical description of a tensor field, going over a publication applying such maths to draw perpendicular lines at random positions in the space. It’s from this tensor that I found the simplest differential equation I could use to simulate my field making a total of 2 months to code and create this generative artwork called Ordinal stream and released on Bitcoin as an Ordinal (NFT) in April 2023.

Tensor are used all over physics or geosciences to build for examples simulations of wind on a map in real time or even in Einstein’s theory of general relativity in which different tensor can describe the trajectory of photons under the influence of mass (gravitation) or moreover the dilation of time due to the particle velocity. Beginning with the building blocks of the project I decided to use Perlin noise to apply acceleration components in an harmonic randomness on every points of the fields so that particles caught in the field would experience forces and start moving drawing then trajectories and abstract patterns. While building my simulation I noticed that sometimes particles on different trajectory were following at the some point the same path which describe the solutions of the differential equation I was using. My program was taking shape and I was facing several problems such as computational difficulty which was requiring computers a lot of computational power making the simulation even slow and I started the long process of optimizing the code to work on the web in Vanilla Javascript (without libraries) and to be able to release the generative artwork as a NFT entirely stored on the Bitcoin Ordinal protocol. The idea was indeed to release particles at random locations and let the field act on them to draw trajectories but was it more efficient to run a loops and release the particles one after another from the coordinates x and y increasing successively or was it more efficient to release them randomly? The solution was actually to create an algorithm that was evaluating the density of streamlines in an defined area and to choose to release the particles or not as the algorithm needed to avoid particles and trajectories overlapping. The algorithm starts by releasing randomly particles and upon a defined density follows the idea of releasing the particles in area with less density. Ultimately 2 loops are ran to fill the remaining space with streamlines to achieve the complete artwork. Integrating the particles position in space and time require an algorithm performing numeric integrations and I choose to use a RK4 (Rutte Kunga) algorithm to do so by translating it from Python to native Javascript which required to build a library for matrix transformations in the same language.

Decided to explore the concept of tensor fields further, I updated my code to apply the simulation to electricity and magnetic fields simulating Maxwell’s equations to draw abstract patterns following electromagnetism. I kind of lost all the data from my dying computer and wasn’t able to release the project. It was that time just before NLP models (Natural Language Processing) and GPTs so the whole code was written from scratch without the help of AI. In the same way I became aware that the pleasure of working on that project would have been completely different with AI knowing that everything is in the process and not the result especially in art and even if the building technic is closely related to the scientific method. Thank you for your help building this project by your never ending support amongst the NFT community.