Crystallization of space: Space-time fractals from fractal arithmetic

详细信息    查看全文

• 作者：Diederik Aerts^a ; Marek Czachor ; ^a ; ^b ; ^{mczachor@pg.gda.pl" class="auth_mail" title="E-mail the corresponding author} ; Maciej Kuna^a ; ^b
• 关键词：Fractals ; Arithmetic ; Space-time
• 刊名：Chaos, Solitons & Fractals
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：83
• 期：Complete
• 页码：201-211
• 全文大小：1789 K

文摘

Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetic allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated with appropriate Lie groups. The construction is illustrated by explicit examples.