Spherical Dendrite by Mark J Stock

The story behind Issue 3’s cover artwork


We are surrounded by complex structures and systems that appear to be lawless and disorderly. Mathematicians try to look for patterns in the seemingly chaotic behaviour and build models that are simple, and yet have the capacity to accurately predict the reality around us. But can a scientific or mathematical model have any artistic value? It seems that the answer is yes. There is a group of digital and algorithmic artists that use science and computational mathematics to create visual art. However, there is an even smaller group of people whose art and science coincide. Meet Mark J Stock.


Chaotic Escape 1 by Mark J Stock

Mark is an artist, scientist, and programmer. His work is heavily influenced by his own research, and he uses scientifically-accurate software to explore “the tension between the natural world and its simulated counterpart, between organic and inorganic, digital and analogue, structure and fluid”. He first started working on simulations and visualisations when working with Moiré patterns—caused by overlaying similar images on top of one another, each offset from the others by some small amount—on a Commodore computer. Mark has a PhD in Aerospace Engineering from the University of Michigan and, unlike some of his colleagues, renounces the use of commercial software for his work. Since much of the reality in the natural world surrounding us is influenced by fluid flow, people are unconsciously tuned into his patterns. Hence one can often see in his art some natural arrangement that we are familiar with. However, unlike in real-life structures, one can run accurate calculations from physically impossible initial conditions, thus creating visually stunning images.

Spherical Dendrite by Mark J Stock

Spherical Dendrite by Mark J Stock

On our cover we have a piece called Spherical Dendrite. It’s one of a series of 50 unique 3D-printed models. This particular model was created from a simulation of “diffusion-limited aggregation constrained to a sphere”. The key element of this process is Brownian motion. This describes the random motion of particles suspended in a fluid, a phenomenon named after botanist Robert Brown who first observed it when looking at pollen grains in water. The mathematical representation of this effect is called the Wiener process. This is a stochastic process that starts at zero, is continuous, and has independent increments that are normally distributed with zero mean and a variance equal to the time steps. It is also used to model noise in electronic engineering, as well as appearing in the Black–Scholes model in the field of finance. To build the object on the cover, virtual particles were introduced into a sphere where they diffused through 3D Brownian motion until they came into contact with an existing part of the structure, sticking to it and eventually producing the final object.

Another recent work by Mark is his Chaotic Escape series. In these images, fluid tries to escape from the centre of a supernova. He describes this process as “like pushing on a string when everything is a string. Chaotic Escape is a series of works from perfect virtual simulations of an impossible condition, created by intricate algorithms, and performed on a desktop supercomputer.”


Mesh #3 Iso by Mark J Stock

Mesh #3 Iso again exploits the freedom of fluid dynamics calculations to work with initial conditions that do not exist in the real world. Hence once again we create a structure that has a familiar behaviour, `despite its obvious artificiality’. The Structure series, from where this piece is taken, strips the fluids portrayed from all of their surrounding visual context, thereby exposing their computational origins.

Thus through Mark’s work, we see the ability of mathematics to free us from the constraints of our physical world; allowing us to use our imagination to merge science and art to create stunning images.


Mark J Stock has been showcasing his work since 2000 and has been in over 80 curated and juried exhibitions since 2001. For more of his art visit http://markjstock.com

(Title image: CF11_1179 by Mark J Stock)

Rudolf Kohulák is a PhD student at UCL working on the modelling of freeze-drying processes.

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