Study 20 · Strange Attractors

RMS Chua System

An artwork linked by title to the Chua family of systems, exploring the visual language of nonlinear mathematical sculpture.

The mathematical reference

RMS Chua is the system name used for this study in the collection. It refers to a mathematical model connected by its name to the Chua family; the artwork does not claim to represent a particular circuit experiment or parameter set. Its role here is to provide a precise starting point for a separate artistic process.

RMS Chua System equations

RMS denotes rotation multiscroll Chua in the Chimpanzee documentation. A folded coordinate transformation acts on a piecewise Chua flow to construct the rail.

dxdt=(3/20)Sₓ[F₁ cos(θ) + F₂ sin(θ)]

dydt=(3/20)F₃

dzdt=(3/20)S𝓏[−F₁ sin(θ) + F₂ cos(θ)]

U = (20/3)(x − 1) − x₀, V = (20/3)z − z₀

X = (|U| + x₀) sin(θ) + (|V| + z₀) cos(θ)

Z = (|U| + x₀) cos(θ) − (|V| + z₀) sin(θ)

F₁ = 10[X − h(Z)]

F₂ = (20/3)y + Z − X, F₃ = −16X

h(u) = mu − mn[sgn(u) + sgn(u − 2n) + sgn(u + 2n)]

Sₓ = (|U + ε| − |U − ε|)/(2ε)

S𝓏 = (|V + ε| − |V − ε|)/(2ε), ε = 0.04

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 RMS Chua 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 takes a technical name out of its usual setting and places it within a gallery context. The result is a digital sculpture to be seen at its own pace: the viewer can trace the contour, notice how light describes the surface and decide what the form suggests. It remains grounded in a mathematical reference while leaving interpretation open.

Modelled in Rhinoceros and rendered in 3ds Max by Riccardo Zerbinati, this vertical work is part of a 40-piece digital collection made without generative AI.

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