Chen System mathematical art by Riccardo Zerbinati explores a chaotic attractor through parametric 3D geometry, form and light.
07 / Strange Attractors · Chen System
Chen System
A study of nonlinear flow that turns a mathematical system into a spatial image.
The Chen System is a well-known three-dimensional chaotic system in nonlinear dynamics. It is related in name and study context to other classic attractors, but this artwork treats it on its own terms: a mathematical source for an independent visual composition. The work is not presented as a scientific diagram or as a simulation of a physical event.
In the Strange Attractors collection, each system becomes an opportunity to examine how mathematical motion might be translated into form. The Chen study invites a viewer to follow the idea of a trajectory through space, then notice how composition and light change the way that structure is perceived.
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The products xy and xz introduce nonlinear feedback. The coefficients determine which trajectories appear; the name alone does not fix the artwork’s shape.
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 Chen 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 closer look
Mathematics → Geometry → Light
From system to image
A strange attractor is a bounded structure that can emerge as a dynamical system evolves. Its motion follows defined rules, yet sensitivity to starting conditions can make a long path difficult to predict. This contrast between structure and uncertainty is one of the ideas explored across the Strange Attractors series.
For Chen System, the named system is a starting point for visual research. Riccardo Zerbinati uses a parametric workflow in Rhinoceros to explore mathematical traces as three-dimensional geometry, then shapes materials, composition and lighting in 3ds Max. The finished image is an authored interpretation of mathematical form, not a scientific plot or an AI-generated image.
Study 07 belongs to a collection of forty vertical digital artworks. View it alongside the other studies to compare how distinct systems can lead to different visual readings.
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