Study 40 · Strange Attractors
Rikitake System
A sculptural interpretation of the Rikitake dynamo system, connecting the collection to mathematical studies of magnetic-field reversals.
The mathematical reference
The Rikitake dynamo model was introduced in Tsuneji Rikitake’s 1958 study of two coupled disk dynamos in relation to Earth’s magnetic field. The paper discusses reversals of electric current and magnetic field in the coupled system. This artwork draws on that scientific reference but is not a simulation of Earth’s field or a plotted trajectory.
Further reading: T. Rikitake, “Oscillations of a system of disk dynamos” (1958), Mathematical Proceedings of the Cambridge Philosophical Society
Rikitake System equations
The coupled variables form a normalized dynamo model. Its time-dependent path becomes the rail for this artwork; the rendered object is not a physical dynamo.
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 Rikitake 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 brings a model rooted in dynamo theory into the intimate scale of a digital sculpture. Its vertical format and reflective surface make a technical subject available through looking: the viewer can notice shape and light first, then follow the title toward its geophysical context. The image is an artistic response, not a claim to reproduce the behaviour of a physical dynamo.
Modelled in Rhinoceros and rendered in 3ds Max by Riccardo Zerbinati, this work belongs to a collection of 40 vertical digital artworks created without generative AI.
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