Yu-Wang System
Yu-Wang System art by Riccardo Zerbinati explores how a time-dependent mathematical path becomes a still image. The reference equations below introduce the named model. Grasshopper samples the trajectory as a three-dimensional rail; a swept cross-section then gives it a surface for the artist’s materials and lighting.
The mathematical reference
The Yu–Wang system is the named mathematical reference for this piece. It situates the work in the wider subject of nonlinear dynamical systems. The image is an artistic interpretation, rather than an experimentally measured object or an exact phase portrait of a specified solution.
Yu-Wang System equations
The exponential term exp(xy) distinguishes this reference from systems that use only polynomial feedback.
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 Yu-Wang 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 rendered sculpture invites the viewer to take time with its silhouette and its changing surface. A neutral setting leaves the form legible; the portrait orientation gives the image a composed, almost object-like presence. The mathematical title offers a way into the work, while its visual character remains open rather than tied to a single explanation.
Modelled parametrically in Rhinoceros and rendered in 3ds Max by Riccardo Zerbinati, this artwork is part of the 40-piece Strange Attractors collection. The process is human-led and uses no generative AI.
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