Premium
Computability of Self‐Similar Sets
Author(s) -
Kamo Hiroyasu,
Kawamura Kiko
Publication year - 1999
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19990450103
Subject(s) - mathematics , computability , set (abstract data type) , euclidean space , euclidean geometry , universal set , discrete mathematics , space (punctuation) , compact space , computable analysis , combinatorics , pure mathematics , computer science , geometry , programming language , operating system
We investigate computability of a self‐similar set on a Euclidean space. A nonempty compact subset of a Euclidean space is called a self‐similar set if it equals to the union of the images of itself by some set of contractions. The main result in this paper is that if all of the contractions are computable, then the self‐similar set is a recursive compact set. A further result on the case that the self‐similar set forms a curve is also discussed.