Mathematician and software developer. My research and tools focus on iterated function systems (IFS), self-affine tiles, and algebraic fractals.
📚 Google Scholar · arXiv · ORCID · 📧 mekhontsev@gmail.com
D. Mekhontsev — The aspect ratio of the Twin Dragon is 1/φ
Preprint, 2026. PDF
C. Bandt, D. Mekhontsev — Elementary fractal geometry. 2. Carpets involving irrational rotations
Fractal and Fractional 6(1), 39, 2022.
C. Bandt, D. Mekhontsev — Computer geometry: Rep-tiles with a hole
The Mathematical Intelligencer 42, 1–9, 2020.
M. Samuel, D. Mekhontsev, A. Tetenov — On dendrites generated by symmetric polygonal systems: The case of regular polygons
Advances in Algebra and Analysis, Springer, 2019.
C. Bandt, D. Mekhontsev — Elementary fractal geometry. New relatives of the Sierpiński gasket
Chaos 28, 063104, 2018.
C. Bandt, D. Mekhontsev, A. Tetenov — A single fractal pinwheel tile
Proceedings of the American Mathematical Society 146(3), 1271–1285, 2018.
D. Mekhontsev — An algebraic framework for finding and analyzing self-affine tiles and fractals
Doctoral thesis, Ernst-Moritz-Arndt-Universität Greifswald, 2019.
IFStile (GPL, C++/C)
A free cross-platform application for the discovery, visualization, and classification of self-similar sets and tessellations. Features:
- Multidimensional IFS construction in arbitrary dimensions (full 2D/3D support)
- Automated fractal discovery: rep-tiles, carpets, dragons, quasicrystal tilings
- Dimensional analysis: Hausdorff dimension via analytical and numerical methods
- Geometric analysis: centroids, moments, aspect ratios of fractal sets
- High-resolution rendering and keyframe animation export
- Declarative domain-specific language AIFS with JavaScript integration
Runs on Windows, macOS, Linux, Android, and WebAssembly.
🌐 ifstile.com · Run in browser
A static reference site cataloguing iterated function systems — definitions,
AIFS programs, interactive fractal renderings, and bibliographic references.
Built with Astro and rendered client-side via ifslib.wasm.