Elementary Fractal Geometry. 2. Carpets Involving Irrational Rotations

Christoph Bandt, Dmitry Mekhontsev

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

Self-similar sets with the open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in the plane, based on rotation by irrational angles. Examples without characteristic directions, with strong connectedness and small complexity, were found in a computer-assisted search. They are surprising since the rotations are given by rational matrices, and the proof of the open set condition usually requires integer data. We develop a classification of self-similar sets by symmetry class and algebraic numbers. Examples are given for various quadratic number fields.

Язык оригиналаанглийский
Номер статьи39
ЖурналFractal and Fractional
Том6
Номер выпуска1
DOI
СостояниеОпубликовано - янв 2022
Опубликовано для внешнего пользованияДа

Предметные области OECD FOS+WOS

  • 1.01.PO МАТЕМАТИКА, МЕЖДИСЦИПЛИНАРНЫЕ ПРИМЕНЕНИЯ

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