Genesio–Tesi System mathematical art by Riccardo Zerbinati transforms a nonlinear system into a parametric 3D study.
09 / Strange Attractors · Genesio–Tesi System
Genesio–Tesi System
A compact mathematical system becomes a starting point for a study of form and instability.
The Genesio–Tesi System is a three-dimensional nonlinear model studied for chaotic dynamics. In this collection, its equations are not displayed as a classroom figure; they provide a structured point of departure for an artwork. The translation from mathematical trace to rendered image creates space for interpretation while keeping the system’s identity in view.
The study holds attention on the relationship between constraint and variation. A defined model gives the exploration a set of rules, while the visual result depends on how the path is sampled, shaped, lit and composed. This makes the work readable both as an entry in a mathematical series and as a digital artwork in its own right.
Enquire about this artwork ↗Explore all 40 studiesGenesio–Tesi System equations
The first two equations link position-like, velocity-like and acceleration-like variables. The final quadratic feedback closes the third-order system.
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 Genesio–Tesi 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 Genesio–Tesi 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 09 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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