Shimizu-Morioka System
Shimizu-Morioka System art by Riccardo Zerbinati explores how a nonlinear trajectory becomes sculptural form. A quadratic term and feedback between coordinates shape the reference model. The artwork develops a sampled rail into a swept surface, with materials and lighting composed in 3ds Max.
The mathematical reference
The Shimizu-Morioka system is a mathematical model studied in nonlinear dynamics. Here its name identifies the work’s point of departure. The image is an original digital sculpture shaped by an interest in how mathematical structures can suggest volume, rhythm and motion.
Shimizu-Morioka System equations
A quadratic term drives z while the xz product feeds that coordinate back into the motion of y.
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 Shimizu-Morioka 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
Rather than asking the image to explain the equations, this study asks what it feels like to look at a form associated with dynamic behaviour. Its metallic surface and neutral setting keep attention on the silhouette and on the way the object seems to turn in space. The reading remains open: the artwork offers a visual encounter, not a scientific diagram.
Created by Riccardo Zerbinati through parametric modelling in Rhinoceros and rendering in 3ds Max, this work belongs to a collection developed through a human-led digital process, without generative AI.
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