This paper is devoted to the study of self-similar fractal rep tiles of the Euclidean planes ℝ2 and ℝ3 using integer matrices. We construct many examples appearing in the literature, as well as new examples by integer matrices. Several exotic and radially symmetric self-similar rep tiles and their variations are obtained with change of bases extending the work by Bandt and others. We also present a few examples of polyhedral self-similar rep tiles including variations.

中文翻译：

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ℝ2 和 ℝ3 使用整数矩阵的分形重复图块

本文致力于研究欧几里得平面的自相似分形块。ℝ2和ℝ3使用整数矩阵。我们构建了许多文献中出现的例子，以及整数矩阵的新例子。几个奇异的和径向对称的自相似重复图块及其变化是通过扩展 Bandt 和其他人的工作的基础的变化获得的。我们还展示了一些包括变体在内的多面体自相似重复图块的示例。