Xing-Yun System
Xing-Yun System art by Riccardo Zerbinati develops a chaotic-system reference into a digital sculpture. Read the model’s reference equations below and follow the process from a sampled trajectory to a swept surface. The artist then composes the geometry in 3ds Max, using material, camera and illumination to make its spatial structure visible.
The mathematical reference
Xing–Yun is the named nonlinear system associated with this study. The title gives the visitor a route into the mathematical context, but this image is an artistic interpretation rather than a direct plot of a specified solution. No parameters or numerical method are claimed for the rendered form.
Xing-Yun System equations
Each equation contains a cubic product. These higher-order interactions supply the mathematical rail before the artist gives it a cross-section, surface and lighting.
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 Xing-Yun 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 piece approaches mathematical inspiration through visual presence. Its upright composition isolates the sculpture; reflected light draws attention to the surface and makes a digital object feel tactile. The name on the page and the open-ended image work together: one offers context, the other invites a personal reading that does not depend on technical expertise.
Created by Riccardo Zerbinati through parametric modelling in Rhinoceros and rendered in 3ds Max, this is one of 40 vertical artworks in a human-led digital collection made without generative AI.
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