Abstract geometrical computation 8: Small machines, accumulations & rationality
作者：
Highlights：
• Signal machines with 2 or less speeds cannot produce accumulations while it is very simple to produce some with 4 speeds.
• A 3-speed signal machine can produce accumulations only if there is some irrational ratio between speeds or positions.
• Euclid algorithm (gcd) is found inside the dynamics. This explains this dichotomy.
摘要
•Signal machines with 2 or less speeds cannot produce accumulations while it is very simple to produce some with 4 speeds.•A 3-speed signal machine can produce accumulations only if there is some irrational ratio between speeds or positions.•Euclid algorithm (gcd) is found inside the dynamics. This explains this dichotomy.
论文关键词：Abstract geometrical computation,Accumulation,Euclidean geometry,Euclid's algorithm,Signal machine,Unconventional computing
论文评审过程：Received 25 April 2016, Revised 11 June 2018, Accepted 13 June 2018, Available online 13 August 2018, Version of Record 13 August 2018.
论文官网地址：https://doi.org/10.1016/j.jcss.2018.06.001
