3 citations · 3 across the 5 of their papers we have counts for
6 papers
The aspect ratio of the Twin Dragon is
Dmitry Mekhontsev
We show that the geometric aspect ratio of the Twin Dragon equals , where is the golden ratio. The result follows by solving the covariance fixed-point equ…
Elementary fractal geometry. Networks and carpets involving irrational rotations
Christoph Bandt, Dmitry Mekhontsev
Self-similar sets with open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in…
Computer geometry: Rep-tiles with a hole
Christoph Bandt, Dmitry Mekhontsev
A cube is an 8-rep-tile: it is the union of eight smaller copies of itself. Is there a set with a hole which has this property? The computer found an interesting and complicated so…
On Dendrites Generated By Symmetric Polygonal Systems: The Case of Regular Polygons
Mary Samuel, Dmitry Mekhontsev, Andrey Tetenov
We define -symmetric polygonal systems of similarities and study the properties of symmetric dendrites, which appear as their attractors. This allows us to find the conditions u…
New relatives of the Sierpinski gasket
Christoph Bandt, Dmitry Mekhontsev
By slight modification of the data of the Sierpinski gasket, keeping the open set condition fulfilled, we obtain self-similar sets with very dense parts, similar to fractals in nat…
A single fractal pinwheel tile
Christoph Bandt, Dmitry Mekhontsev, Andrei Tetenov
The pinwheel triangle of Conway and Radin is a standard example for tilings with self-similarity and statistical circular symmetry. Many modifications were constructed, all based o…