04 / Strange Attractors · Thomas System
Thomas System
A cyclic system becomes an invitation to look for rhythm, recurrence and balance in three dimensions.
The Thomas System is associated with a cyclically symmetric form of nonlinear dynamics. That sense of recurrence gives this study its curatorial point of departure: a mathematical rule can return to itself without producing a static image. The artwork asks how such a rhythm might be experienced as a spatial object.
Rather than illustrating a formula, the composition translates the idea of a repeating process into digital geometry. Light and perspective encourage the viewer to move between the whole structure and its individual turns. The result is deliberately open: it can be read as a trace of motion, a sculptural volume or an abstract study in balance.
Enquire about this artwork ↗Explore all 40 studiesThomas System equations
The same sine-and-damping rule cycles through x, y and z, giving this reference system its cyclic symmetry.
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 Thomas 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 Thomas 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 04 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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