Three-Scroll Unified Chaotic System 2
TSUCS 2 — Three-Scroll Unified Chaotic System 2 — is Study 23 by Riccardo Zerbinati. The Chimpanzee component documentation also labels TSUCS 2 as Dequan Li System. The artwork develops a sampled trajectory into swept 3D geometry, then uses material and light to reveal the hidden beauty of chaos theory.
The mathematical reference
The title identifies the system and variant used as the mathematical point of departure for this artwork. The term “three-scroll” names a type of structure discussed in studies of chaotic systems, but the image here is not a numerical phase portrait or an independently verified simulation. It is a digital artwork shaped by mathematical inspiration.
TSUCS 2: reference equations
This formulation belongs to the Dequan-Li/TSUCS family. Different coefficient choices can produce qualitatively different motion, so three-scroll naming is not a claim that every parameter choice is chaotic.
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 TSUCS 2 trajectory to 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
As the second piece in this named sequence, the work invites a visual comparison with its companion. The vertical composition gives the object a strong, self-contained presence, while the reflective metallic finish suggests volume and surface. The viewer can study the outline and its turns without needing to read the form as a literal explanation of the equations.
Created by Riccardo Zerbinati with parametric modelling in Rhinoceros and rendering in 3ds Max, this work is one of 40 vertical artworks in a human-led collection made without generative AI.
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