Rabinovich-Fabrikant System
Rabinovich-Fabrikant System art by Riccardo Zerbinati interprets a nonlinear trajectory as sculptural geometry. The reference equations below introduce the named model. A sampled rail becomes a swept surface in Grasshopper, while the artist’s material, camera and lighting choices in 3ds Max shape the final image.
The mathematical reference
The Rabinovich–Fabrikant equations are named after Mikhail Rabinovich and Anatoly Fabrikant. Their 1979 paper, “Stochastic self-modulation of waves in nonequilibrium media,” provides the research context behind this system. The artwork is a separate visual interpretation, not a reproduction of the paper’s analysis or a computed trajectory.
Further reading: M. I. Rabinovich and A. L. Fabrikant, “Stochastic self-modulation of waves in nonequilibrium media” (1979), JETP
Rabinovich-Fabrikant System equations
The cubic terms and z-dependent coupling shape this three-variable flow. Numerical trajectories can depend strongly on both the parameters and integration choices.
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 Rabinovich-Fabrikant 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 title points to the mathematical ideas beneath the work, while the image invites a different kind of attention. Its metallic appearance suggests an object with mass, though it exists as a digital model and render. In this study, the passage from nonlinear equations to a sculptural image remains visible as a translation between disciplines rather than a one-to-one illustration.
Modelled in Rhinoceros and rendered in 3ds Max by Riccardo Zerbinati, this work belongs to a collection of 40 vertical digital artworks created without generative AI.
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