Self-Similar Groups

Part of the Compact Textbooks in Mathematics book series (CTM)


Self-similar groups, or automata groups, consist of certain automorphisms of the infinite complete rooted binary tree. We describe them using several different concepts: computers are designed, portraits are drawn, and self-similar rules are written. Some well-known self-similar groups such as Grigorchuk’s group, the Adding Machine, and the Tower of Hanoi are explored.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Math and Computer ScienceNew York City College of Technology, The City University of New YorkBrooklynUSA
  2. 2.Department of MathematicsBorough of Manhattan Community College, The City University of New YorkNew YorkUSA
  3. 3.Department of MathematicsMonroe Community CollegeRochesterUSA

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