Study 27 · Strange Attractors

3-Cell CNN

An artwork inspired by a three-cell cellular neural network, translating an electronics research reference into sculptural form.

The mathematical reference

A 1992 IEEE conference paper reports a chaotic attractor arising from an autonomous three-cell cellular neural network and describes a structure similar to the double-scroll attractor. That is the research context behind this title. The artwork is a visual interpretation, not the paper’s graph, circuit or experimental record.

Further reading: F. Zou and J. A. Nossek, “Double scroll and cellular neural networks” (1992).

3-Cell CNN System equations

CNN means cellular neural network here. The cells are coupled differential equations with a saturation function; the label does not imply that generative AI produced the artwork.

dxdt=−x + p₁f(x) − sf(y) − sf(z)

dydt=−y − sf(x) + p₂f(y) − rf(z)

dzdt=−z − sf(x) + rf(y) + p₃f(z)

f(u) = ½(|u + 1| − |u − 1|)

Here, t is time and the variables are coordinates in the system’s state space. Letters such as a, b and c denote fixed coefficients. These are reference equations for the named model or family, not a recovered record of the parameters, initial conditions or integration settings used in this particular image. Chaotic behaviour depends on those choices.

Formula reference: View the documented system and source.

From a trajectory to 3-Cell CNN System art

Riccardo develops the rail in Grasshopper for Rhinoceros using Chimpanzee. The system evolves over time, producing successive three-dimensional points. Connecting those samples creates a path. A cross-section is then swept along that rail, giving the line thickness and a surface. This is how a time-dependent mathematical trajectory becomes visible as sculptural geometry.

The sweep adds a visual layer to the mathematics: its width and orientation affect how the form catches light. Riccardo then uses 3ds Max to develop the material, camera and illumination. The finished work is a digital render of this geometry, rather than a photograph of a fabricated object. No generative AI is used to create the artwork.

To read the image, follow a single edge as it moves through light and shadow. Notice where the projected path overlaps, opens or disappears behind another surface. The rail comes from a rule evolving through time; the artist’s composition lets us experience that motion as a still image. The aim is to reveal the hidden beauty of chaos theory.

A study in form

The work shifts this technical reference into a gallery setting. A metallic surface suggests material and weight, while the portrait format isolates the image for closer attention. Viewers can recognise the scientific origin in the title and still approach the rendered sculpture on its own terms—as an arrangement of contour, volume and light rather than a scientific diagram.

Modelled in Rhinoceros and rendered in 3ds Max by Riccardo Zerbinati, this is one of 40 works made through a human-led digital process without generative AI.

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