Study 32 · Strange Attractors
Bouali 3 System
A third Bouali system study in the collection, exploring how a repeated mathematical reference can lead to a distinct sculpture.
The mathematical reference
Bouali 3 is the designation used for this third study in a sequence of works. The number distinguishes it within the collection, while the system name supplies its mathematical point of departure. The artwork does not claim to be an exact simulation or a scientific plot; it is a separately modelled visual response.
Bouali 3 System equations
The quadratic xy and cubic x²y terms coexist with a particularly simple third equation. This is Bouali’s published four-parameter reference.
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 Bouali 3 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
Placed beside the earlier Bouali studies, the image supports comparison across a related set without collapsing the pieces into copies. Each work is encountered as its own object, with a separate silhouette and visual rhythm. The metallic rendering and quiet presentation keep attention on form, inviting viewers to notice both continuity and difference.
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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