storytelling (systems thinking):
https://www.tg-me.com/storytellingsystemsthinking

demonstrators:
https://www.tg-me.com/systemsdemonstrators

sharing and reposts:
https://www.tg-me.com/systemssharing

talks and writings:
https://www.tg-me.com/stochastictheoryofcommunication

cybernetic culture:
https://www.tg-me.com/communicationsdevelopment

books and papers:
https://www.tg-me.com/booksonsysapproaches

basics and elements:
https://www.tg-me.com/elementsofsysapproaches

Sierpiński triangle and Games of Chaos with pygame

Glider Gun with pygame

Conway's Game of Life with pygame

Maxwell–Boltzmann
distribution
with
Matplotlib

#distribution #thermodynamics #complexsystems #multiagent

Overture for the Stochastic Theory of Communication with matplotlib widgets and matplotlib animations


Description:

State of a cell is represented as RGB. Number of possible states (state space size) for each cell is limited to alphabet_size^number_of_parameters = 3^3 = 27.

alphabet_size = 3 ({0, 1, 2})
number_of_parameters = 3 (R, G, B)

Base rule (connection): 1. none of two cells in the neighborhood can have same state. 2. if no possible states remain, cell keeps its state.

#entropy #communication #synergy #selforganization #multiagent

Not-self-intersecting trajectory
with
matplotlib

#trajectory #phasespace #projection #torus #matplotlib

Inspiration

This animation draws a curve

z(θ) = exp(iθ) + exp(i𝝅θ),

where θ ∈ ℝ, z ∈ ℂ.


1 Harmonics with an irrational ratio of frequencies:

exp(iθ) and exp(i𝝅θ) are periodic functions that draw cycles on the complex plane. But since the ratio of their frequencies 𝝅θ and θ is irrational 𝝅θ / θ = 𝝅, their phases relation never repeats. By the time the first harmonic exp(iθ) completes one full turn (θ = 2𝝅), the second harmonic exp(i𝝅θ) has been rotated by 2𝝅² radians.

This irrationality (transcendentality is not necessary actually) of frequencies' ratio (namely of 𝝅 in this example) explains why the curve z(θ) from the animation is quasiperiodic and never closes.


2 Self-intersecting projection of not-self-intersecting curve:

Observing that the curve z(θ) never closes, I thought that there might be some other curve mapped in z(θ) that lives in another space of higher dimension and never intersects itself.

(I remembered the Lorenz curve that is not-self-intersecting and thought that there might be some chaotic features found in a transcendentality of 𝝅. But there are not. Actually the behaviour observed in the animation is quasiperiodic and not chaotic.)

With the help of GPT I found out that the not-self-intersecting curve I was looking for is

θ↦(exp(iθ), exp(i𝝅θ)) ∈ ℂ²
and
z(θ) = exp(iθ) + exp(i𝝅θ) is its ℂ¹ projection.

In order to somehow visualise the curve (exp(iθ), exp(i𝝅θ)) I considered a torus that it wraps around. exp(iθ) and exp(i𝝅θ) trace out circles in two orthogonal complex planes. The first circle revolves with frequency θ, while the second - with 𝝅θ. These frequencies can then be used as angles for parameterization of torus in ℝ³ and it's visualisation.

Energy Gradient Relaxation and Entropy Increase

Discussed with chatgpt connection between information theory and thermodynamics and other complex systems stuff (the code for animation is also there)

Chapter 7 Thermodynamics of Complex Systems

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