Tootfinder

Post-apocalyptic computing from cellular automata
Genaro J. Martinez, Andrew Adamatzky, Guanrong Chen
https://arxiv.org/abs/2508.06035 https://arxiv.org/pd…

Post-apocalyptic computing from cellular automata
Cellular automata are arrays of finite state machines that can exist in a finite number of states. These machines update their states simultaneously based on specific local rules that govern their interactions. This framework provides a simple yet powerful model for studying complex systems and emergent behaviors. We revisit and reconsider the traditional notion of an algorithm, proposing a novel perspective in which algorithms are represented through the dynamic state-space configurations of c…

Replaced article(s) found for nlin.SI. https://arxiv.org/list/nlin.SI/new
[1/1]:
- Inverse scattering transform for the defocusing nonlinear Schr\"{o}dinger equation with local and...
Chuanxin Xu, Tao Xu, Min Li

Integrable deformations of cluster maps of type $D_{2N}$
Wookyung Kim
https://arxiv.org/abs/2506.06182 https://arxiv.org/pdf/2506.061…

Integrable deformations of cluster maps of type $D_{2N}$
In this paper, we extend one of the main results in \cite{hkm24}, of a deformed type $D_{4}$ map, to the general case of the type $D_{2N}$ for $N\geq3$. This can be achieved through a "local expansion" operation, introduced in the joint work \cite{grab} with Grabowski and Hone. This operation involves inserting a specific subquiver into the quiver arising from the Laurentification of the deformed type $D_{4}$ map. This insertion yields a new quiver, obtained through the Laurentification of the …

Analysis of the Chaotic Itinerancy Phenomenon using Entropy and Clustering
Nikodem Mierski, Pawe{\l} Pilarczyk
https://arxiv.org/abs/2507.22643 https://arx…

Analysis of the Chaotic Itinerancy Phenomenon using Entropy and Clustering
We introduce a new methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. We determine systems likely to experience chaotic itinerancy by means of local Shannon entropy and local permutation entropy. In such systems, we find quasi-stable states (attractor ruins) and chaotic transition states using a density-based clustering algorithm. Our approach then focuses on examining the chaotic itinerancy dynamics…

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…

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…

Higher-Order Transverse Discontinuity Mapping in Filippov Systems: Analysis and Experimental Validation using an Electronic Circuit
Rohit Chawla, Soumyajit Seth, Aasifa Rounak, Vikram Pakrashi
https://arxiv.org/abs/2506.18379

Higher-Order Transverse Discontinuity Mapping in Filippov Systems: Analysis and Experimental Validation using an Electronic Circuit
This paper shows that linearizing the transverse discontinuity mapping (TDM) in Filippov systems can produce inaccurate predictions of the dynamics in impact oscillators operating near a pre-stressed soft barrier. This discrepancy arises from the limitations of the linearized saltation matrix, which inaccurately predicts impacts in the local neighborhood of the discontinuity boundary. To address this issue, a higher-order approximation of the TDM is derived, which accurately captures the onset …

Replaced article(s) found for nlin.CG. https://arxiv.org/list/nlin.CG/new
[1/1]:
- Fast offline decoding with local message-passing automata
Ethan Lake

Replaced article(s) found for nlin.SI. https://arxiv.org/list/nlin.SI/new
[1/1]:
- Evolution of internal cnoidal waves with local defects in a two-layer fluid with rotation
Korsarun Nirunwiroj, Dmitri Tseluiko, Karima Khusnutdinova

Invariant Reduction for Partial Differential Equations. III: Poisson brackets
Kostya Druzhkov
https://arxiv.org/abs/2507.08213 https://

Invariant Reduction for Partial Differential Equations. III: Poisson brackets
We show that, under suitable conditions, finite-dimensional systems describing invariant solutions of partial differential equations (PDEs) inherit local Hamiltonian operators through the mechanism of invariant reduction, which applies uniformly to point, contact, and higher symmetries. The inherited operators endow the reduced systems with Poisson bivectors that relate constants of motion to symmetries. Applying the same mechanism to invariant conservation laws, we further show that the induce…