Two-Box Bit Visualization. Energy Gradient Relaxation and Entropy Increase

Discussed with chatgpt connection between information theory and thermodynamics

The animation is a microscopic parable of how energy flow, probability bias, entropy reduction, and emergent order are inseparably linked—exactly the mechanism through which complex structures arise in nature according to Prigogine’s theory of dissipative systems.

Chapter 7 Thermodynamics of Complex Systems

#energy #probability #distribution #entropy #information #thermodynamics #complexsystems

Cellular automatons are
a classic example of models
in which complex behavior
arises from very simple rules
of state transition.

• The animation above draws
one dimensional automaton
evolving in time according to
one of Wolfram's rules of
transition which can be set in
interactive mode.
• The model considers mapping
between a cell and its
neighbourhood consisting of
the cell itself, the left neighbour
of the cell and the right one.
• While a state space of one cell
is {0, 1} and the neighborhood
consists of three cells, there are 8
possible configurations of the
collective state of the
neighborhood.
• These configurations are listed
in the first row of the table on
the bottom of the animation
window.
• And the second row of the table
is filled with cell's state at next
discrete moment of time
depending on the state of cell's
neighbourhood. This string of 8
bits is a binary representation of
rule number which can be set in
the box on the left bottom of the
window.
• Since there are 8 possible
configurations of neighbourhood
state, the rule is 8-bit number,
what means that there are 256
possible rules.
• Each rule cause a distinct type
of dynamical behaviour of the
automaton.

The animation was inspired by
Chapter 2 (Simple Rules) of
this Complex Systems book

Some related scripts and other resources are stored in this repository. Run animations, explore, develop, copy, and use algorithms and their implementations.

https://github.com/LyFX5/simsim

Some Python tools for developing simulations and visualizations

IR-SIM
Python-based lightweight robot simulator designed for navigation, control, and reinforcement learning
(https://github.com/hanruihua/ir-sim)

PufferLib
Simplifying reinforcement learning for complex game environments
(https://github.com/PufferAI/PufferLib)

Φ_Flow
A differentiable PDE solving framework for machine learning
(https://github.com/tum-pbs/PhiFlow)

Pygfx
Powerful and versatile visualization for Python
(https://github.com/pygfx/pygfx?tab=readme-ov-file)

"Turing patterns in social systems are ordered structures that emerge from chaotic, disorderly interactions.

According to American mathematician Martin Short and his colleagues, Turing patterns can also be observed in human communities organized by social feedback on behavior and movement. For example, they are used to explain the phenomenon of crime “hot spots” - areas with abnormally high crime rates.

Turing patterns are also found in prehistoric and ancient art, including petroglyphs, cave paintings, and patterns on vases and other objects.

In addition, researchers have found similar properties in the distribution of species in ecological systems, such as the predator-prey model, in which victims work as activators, multiplying and increasing their numbers, and predators work as inhibitors, regulating population size. "

Turing Patterns and Reaction Diffusion Equations (blogpost with explanation and python implementation)

There is no local church

By the way