Study 12 · Strange Attractors
Rucklidge System
A visual interpretation of the Rucklidge system, bringing nonlinear mathematics into a considered, vertical sculptural composition.
The mathematical reference
The title connects this work to the Rucklidge system, a named model in the study of nonlinear dynamics. The artwork does not show experimental data. It uses mathematical inspiration to guide an independent modelling and rendering process, translating an abstract point of reference into a visible object.
Rucklidge System equations
The y² term and yz coupling provide the nonlinearity in this compact three-variable model.
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 Rucklidge 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
In portrait format, the object reads as a concentrated encounter between line, volume and light. A metallic finish gives the form a tangible quality, while its digital construction keeps it slightly outside the everyday world. The result invites the viewer to follow the shape and return to it.
Created by Riccardo Zerbinati through parametric modelling in Rhinoceros and rendering in 3ds Max, this work belongs to a collection developed through a human-led digital process, without generative AI.
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