Category: Hic et Nunc (HEN)

Cellular Neural Networks or Cellular Nonlinear Networks (CNN) are similar to Cellular Automata (CA): a grid of cells that evolve in time with local interactions with neighbouring cells.

Instead of a finite number of states for each cell (as for the CA) in CNN the cells can assume continuous values given from a chaotic oscillator and the local interactions are due to the coupling of oscillators in neighbouring cells.

With CNN is possible to model a number of physical systems described by Partial Differential Equations: Wave propagation, Heat Diffusion, Chemical Reaction-Diffusion and the likes.

In this case we have a Lorenz chaotic oscillator on each cell coupled with the 8 neighbouring oscillators.

The initial conditions, boundary conditions and coupling constant are chosen in such a way to obtain symmetrical patterns.

Here the CNN is rendered as a surface with a colormap from matplotlib (twilight).

The rendering is by means of a C++ program with openFrameworks toolkit.

https://objkt.com/asset/hicetnunc/639680

Cellular Neural Networks or Cellular Nonlinear Networks (CNN) are similar to Cellular Automata (CA): a grid of cells that evolve in time with local interactions with neighbouring cells.

Instead of a finite number of states for each cell (as for the CA) in CNN the cells can assume continuous values given from a chaotic oscillator and the local interactions are due to the coupling of oscillators in neighbouring cells.

With CNN is possible to model a number of physical systems described by Partial Differential Equations: Wave propagation, Heat Diffusion, Chemical Reaction-Diffusion and the likes.

In this case we have a Lorenz chaotic oscillator on each cell coupled with the 8 neighbouring oscillators.

The initial conditions, boundary conditions and coupling constant are chosen in such a way to obtain symmetrical patterns.

Colormap from matplotlib (flag).

The rendering is by means of a C++ program with openFrameworks toolkit.

https://objkt.com/asset/hicetnunc/609607

Cellular Automata (CA) model for Belousov–Zhabotinsky (BZ) Reaction Diffusion system.
In BZ system non linear chemical oscillators give rise to pattern formation, large scale ordered patterns emerge from chaotic initial conditions.
The CA model gives rise to spiral waves patterns using only local interactions.
The periodic boundary conditions used in the CA gives a natural mapping on a torus.

https://objkt.com/asset/hicetnunc/593315