Proof

...math is beautiful!

Flow 9 by Andy Lomas
This image is composed of the layered trajectories followed by millions of particles.    Each individual trajectory is essentially an independent random process, with    the trail terminating when it reaches a deposition zone. Collectively the paths    combine to form delicate complex shapes of filigree and shadow in the areas    of negative space that the paths don’t reach.  Over time, as particles deposit they create a growing region that future particles    will not be able to enter. There are no actual defined boundaries, simply intricately    structured gradients of tone formed by the end points of trajectories.
Andy Lomas, Digital Artist, London  “These pieces are part of a study into how complex organic forms can be created    from simple mathematical rules.
The base algorithms used to generate the forms are variations on Diffusion    Limited Aggregation. Different structures are produced by introducing small    biases and changes to the rules for particle motion and deposition. The growth    like nature of the process, repeatedly aggregating on top of the currently deposited    system, produces reinforcement of deviations caused by forces applied to the    undeposited particles as they randomly move. This means that small biases to    the rules and conditions for growth can produce great changes to the finally    created form.  All the software used to simulate the structures and render the final images    was written by the artist in Visual C++.”

Flow 9 by Andy Lomas

This image is composed of the layered trajectories followed by millions of particles. Each individual trajectory is essentially an independent random process, with the trail terminating when it reaches a deposition zone. Collectively the paths combine to form delicate complex shapes of filigree and shadow in the areas of negative space that the paths don’t reach.

Over time, as particles deposit they create a growing region that future particles will not be able to enter. There are no actual defined boundaries, simply intricately structured gradients of tone formed by the end points of trajectories.

Andy Lomas, Digital Artist, London

“These pieces are part of a study into how complex organic forms can be created from simple mathematical rules.

The base algorithms used to generate the forms are variations on Diffusion Limited Aggregation. Different structures are produced by introducing small biases and changes to the rules for particle motion and deposition. The growth like nature of the process, repeatedly aggregating on top of the currently deposited system, produces reinforcement of deviations caused by forces applied to the undeposited particles as they randomly move. This means that small biases to the rules and conditions for growth can produce great changes to the finally created form.

All the software used to simulate the structures and render the final images was written by the artist in Visual C++.”

Notes:

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