Mathematician and software developer. My research and tools focus on iterated function systems (IFS), self-affine tiles, and algebraic fractals.

📚 Google Scholar · arXiv · ORCID · 📧 [email protected]

D. Mekhontsev — Disk-Like Self-Similar Tiles with High Boundary Dimension
Preprint, 2026. PDF

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.

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.

🌐 ifsdb.github.io · source