Tootfinder

Loop Patterns Formed by Cellular Automata
Rolf Hoffmann, Mariusz Bia{\l}ecki
https://arxiv.org/abs/2505.22679 https://arxiv.org/pdf/2…

Loop Patterns Formed by Cellular Automata
A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain several loops that are not allowed to touch each other. The problem is solved by designing an appropriate set of tiles that can overlap and which are used in the CA rule. Templates are derived from the tiles which are used for local pattern matching. In order to dr…

On novel Hamiltonian description of the nonholonomic Suslov problem
A. V. Tsiganov
https://arxiv.org/abs/2505.19594 https://arxiv.org…

On novel Hamiltonian description of the nonholonomic Suslov problem
We present some new Poisson bivectors that are invariants by the flow of the nonholonomic Suslov problem. Two rank four invariant Poisson bivectors have globally defined Casimir functions and, therefore, define cubic Poisson brackets on the five dimensional state space with standard symplectic leaves. For the Suslov gyrostat in the potential field we found rank two Poisson bivectors having only two globally defined Casimir functions and, therefore, we say about formal Hamiltonian description in…

Loop Patterns Formed by Cellular Automata
Rolf Hoffmann, Mariusz Bia{\l}ecki
https://arxiv.org/abs/2505.22679 https://arxiv.org/pdf/2…

Loop Patterns Formed by Cellular Automata
A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain several loops that are not allowed to touch each other. The problem is solved by designing an appropriate set of tiles that can overlap and which are used in the CA rule. Templates are derived from the tiles which are used for local pattern matching. In order to dr…