Study 22 · Strange Attractors
Bouali 2 System
A second Bouali system study, translating a reference from nonlinear dynamics into a vertical, reflective digital sculpture.
The mathematical reference
Bouali 2 is the system designation used for this work in the Strange Attractors collection. Its title provides the mathematical reference, but not a claim that the picture is a phase portrait or simulation output. The artwork translates an abstract starting point into an independent visual object.
Bouali 2 System equations
The x²y term and xz feedback extend a two-variable oscillator into three dimensions. The reference formula keeps the parameters symbolic rather than assigning the artwork a reconstructed parameter set.
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 2 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
As the second work associated with this name, the piece belongs to a sequence that encourages comparison. Its portrait framing gives the composition a contained presence, while a reflective surface makes the digital form feel almost tangible. Viewers can approach it through the mathematical context or focus on how the rendered object occupies space and catches light.
Modelled in Rhinoceros and rendered in 3ds Max by Riccardo Zerbinati, this work is one of 40 vertical artworks in a collection made without generative AI.
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