Dynamic Mandelbulb fractals: A mathematical framework for time-evolving 3D fractals using distance estimation

Anurag Kumar and L. Bhaskar

Chaos, Solitons & Fractals, 2025, vol. 199, issue P3

Abstract: This paper presents a novel approach to generating a time-dependent Mandelbulb fractal by introducing dynamic spatial transformations within its iterative construction process. By embedding smoothly varying sinusoidal translations-scaled by both global time and iteration index and synchronizing a phase-driven rotation in the XY-plane with Greenwich Mean Time, the fractal’s internal geometry undergoes continuous, organic deformation while preserving its core self-similar patterns. Leveraging a distance-estimator based raymarching pipeline in GLSL, our implementation renders these evolving structures in real time, allowing detailed exploration of their richly evolving forms.

Keywords: Fractal; Mandelbrot set; Mandelbulb fractal; Dynamic Mandelbulb fractals (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077925008422
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p3:s0960077925008422

DOI: 10.1016/j.chaos.2025.116829

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().