Study 18 · Strange Attractors

RMW Lorenz System

A sculptural interpretation of the RMW Lorenz system, extending this collection’s dialogue with nonlinear mathematical forms.

The mathematical reference

RMW Lorenz identifies a variant associated with the Lorenz family of mathematical systems. The label provides the reference for this artwork; it does not specify a parameter set or claim that the image is a numerical phase portrait. It is an artistic response developed through three-dimensional modelling and rendering.

RMW Lorenz System equations

RMW denotes the rotation multiwing Lorenz family in the Chimpanzee documentation. The auxiliary variables fold and rotate the coordinates, while the switching function F creates the multiwing structure.

dxdt=Hₓ[H₁ cos(θ) + H₃ sin(θ)]

dydt=H₂

dzdt=H𝓏[−H₁ sin(θ) + H₃ cos(θ)]

X = (|x − x₀| + x₀) cos(θ) − (|z − z₀| + z₀) sin(θ)

Z = (|x − x₀| + x₀) sin(θ) + (|z − z₀| + z₀) cos(θ)

H₁ = 100(y − 0.1X)

H₂ = 0.1(24 − 4c)X − 0.1pXZ + cy

H₃ = F(X) − (8/3)Z

F(X) = 0.01F₀X² − ∑ᵢ₌₁ᴺ Fᵢ[1 + ½sgn(0.1X − Eᵢ) − ½sgn(0.1X + Eᵢ)]

Hₓ = (|x − x₀ + ε| − |x − x₀ − ε|)/(2ε)

H𝓏 = (|z − z₀ + ε| − |z − z₀ − ε|)/(2ε), ε = 0.0004

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 RMW Lorenz 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

Placed alongside the Lorenz study, this work invites comparison without asking the viewer to treat the images as scientific evidence. The metallic surface and vertical presentation turn the shape into an object for sustained looking. Differences between works can be noticed as differences in visual character, while the shared process makes them part of one considered series.

Modelled in Rhinoceros and rendered in 3ds Max by Riccardo Zerbinati, this work is one of 40 vertical artworks in the Strange Attractors collection, created through a human-led process without generative AI.

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