Liu-Chen System
Liu-Chen System art by Riccardo Zerbinati connects a nonlinear-system reference with a sculptural study of motion and form. The equations below provide mathematical context. Sampling the evolving trajectory produces a 3D rail; sweeping a cross-section along it gives the artist a surface to compose through materials and light.
The mathematical reference
The Liu–Chen system is the named mathematical point of departure for this work. The image belongs to an artistic collection informed by equations and dynamical systems, but it should not be mistaken for an experimental measurement or a direct, parameter-specific phase portrait.
Liu-Chen System equations
This is a generalized reference form used in a dynamical-systems implementation. Several sign conventions and extensions circulate as Liu–Chen; the coefficients are symbolic and are not a reconstruction of the studio settings.
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 Liu-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 study in form
This study turns a technical reference into a quiet visual encounter. The viewer can take in the object as a whole, then follow the changes in its contour and the way its reflective surface catches light. In this gallery setting, mathematical context and visual autonomy are allowed to sit side by side.
Modelled in Rhinoceros and rendered in 3ds Max by Riccardo Zerbinati, this is one of 40 vertical digital works in the Strange Attractors collection. The creative process is human-led and uses no generative AI.
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