Study 13 · Strange Attractors
Lorenz System
A sculptural study inspired by the Lorenz system, a classic model of convection and sensitive dependence in nonlinear dynamics.
The mathematical reference
Edward N. Lorenz’s 1963 paper examined a simplified model of atmospheric convection. It showed nonperiodic solutions sensitive to small changes in initial conditions. The Lorenz attractor is a trajectory in phase space, not a physical object. This artwork draws on that mathematical history but is an independent digital sculpture, not a plot or a weather forecast.
Further reading: E. N. Lorenz, “Deterministic Nonperiodic Flow” (1963).
Lorenz System equations
Two product terms, xy and xz, couple three changing variables. Lorenz’s convection model is a foundational example of deterministic motion with sensitive dependence on initial conditions.
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 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 portrait composition gives this mathematical reference a tangible presence. Rendered metal invites a slower kind of looking than a chart: the eye can follow the form as if moving around a sculpture. The system’s name provides a precise point of departure; its visual translation leaves room for a personal reading.
Created by Riccardo Zerbinati through parametric modelling in Rhinoceros and rendered in 3ds Max, this work is one of 40 vertical digital artworks in the Strange Attractors collection. The practice is human-led and uses no generative AI.
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