Study 15 · Strange Attractors
Arneodo System
An artwork inspired by the Arneodo system, exploring how a reference from nonlinear mathematics can become an independent digital sculpture.
The mathematical reference
“Arneodo system” identifies a mathematical reference associated with nonlinear dynamics. The artwork’s title points visitors toward that context, while the visual object remains an artistic interpretation. It should not be read as measured data or as a direct illustration of a particular solution unless a specific parameter set and rendering method are supplied.
Arneodo System equations
The first two equations pass motion between successive variables. A cubic term supplies the nonlinear feedback in the third equation.
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 Arneodo 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
This study focuses on the passage from abstraction to presence. In a vertical format, the image can be approached as a self-contained object: its contours invite the eye to move, pause and return. The cool metallic treatment adds a sense of materiality to a form that exists through digital modelling and light. The artwork offers a meeting point between mathematical curiosity and visual attention.
Created by Riccardo Zerbinati through parametric modelling in Rhinoceros and rendered in 3ds Max, this is one of 40 vertical works in the Strange Attractors collection. The process is human-led and uses no generative AI.
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