Study 26 · Strange Attractors
Proto-Lorenz System
A sculptural study associated with the Lorenz family of nonlinear systems, using mathematical inspiration as a starting point for form.
The mathematical reference
“Proto-Lorenz” is the title used for this study in the collection. It signals a connection to the broader Lorenz family of nonlinear models, while leaving the exact parameterisation and computational method unspecified. The image is an independent artistic interpretation, not a verified trajectory or a historical scientific illustration.
Proto-Lorenz System equations
The displayed equations are the original quotient formulation of proto-Lorenz. They identify opposite points of the Lorenz flow. Higher-cover formulas also appear under this name; this reference does not identify the covering used for this artwork.
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 Proto-Lorenz 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 work invites a comparison with other Lorenz-named studies in the collection. Rather than repeating a textbook diagram, it gives the reference a rendered, sculptural presence. Its vertical composition allows the viewer to take in the object as a whole before following the details of its contour and the way its surface catches light.
Created by Riccardo Zerbinati through parametric modelling in Rhinoceros and rendering in 3ds Max, this is one of 40 vertical works made without generative AI.
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