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Visualization of Mandelbulbs Associated with the Zeta Functions
Pub. online: 18 September 2026      Type: Research Article      Open accessOpen Access
Received
1 March 2026
Accepted
1 July 2026
Published
18 September 2026

Abstract

This research builds upon our previous work on efficient algorithms for calculating and visualizing fractal structures associated with zeta functions, shifting the focus from two-dimensional to three-dimensional structures. Specifically, we introduce Zetabulbs – a class of Mandelbulbs (three-dimensional analogues of Mandelbrot sets) derived from the zeta functions. The visualization of Mandelbulbs poses substantial computational and algorithmic challenges, while also carrying practical relevance in areas such as digital visual effects, where Mandelbulb-based structures have been used in the production of high-budget films. By introducing Zetabulbs, we expand the landscape of zeta-function–driven fractal geometry and open new opportunities for its application in both artistic visualization and scientific exploration.

References

 
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Belovas, I., Sabaliauskas, M., Kuzma, L. (2022). Series with binomial-like coefficients for the investigation of fractal structures associated with the Riemann zeta function. Fractal and Fractional, 27(1). https://doi.org/10.3390/fractalfract6060300.
 
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Biographies

Kuzma Lukas
https://orcid.org/0000-0002-6502-7787
lukas.kuzma@mif.vu.lt

L. Kuzma received his master’s degree in computing from Vilnius University in 2024. He is currently a PhD student at the Institute of Data Science and Digital Technologies, Faculty of Mathematics and Informatics, Vilnius University. His research interests include computational problems related to zeta functions.

Belovas Igoris
https://orcid.org/0000-0002-0478-1102
igoris.belovas@mif.vu.lt

I. Belovas received his doctoral degree in mathematical sciences from Vilnius Gediminas Technical University and the Institute of Mathematics and Informatics in 2004. He is currently a professor at the Institute of Data Science and Digital Technologies, Faculty of Mathematics and Informatics, Vilnius University. His research interests include problems in analytical number theory and financial engineering.

Sabaliauskas Martynas
https://orcid.org/0000-0001-5456-7844
martynas.sabaliauskas@mif.vu.lt

M. Sabaliauskas received his doctoral degree in technological SCiences from Vilnius University in 2017. He is currently an associate professor at the Institute of Data Science and Digital Technologies, Faculty of Mathematics and Informatics, Vilnius University. His research interests include problems in 3D visualization.


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Copyright
© 2026 Vilnius University
Open access article under the CC BY license.

Keywords
fractal structures numerical algorithms zeta functions visualizations Zetabulbs

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