Causal loop diagram based on my Gemini interaction Feb 2026 around Richard Soutwell's video Category Theory For Beginners: All Concepts, using Gene Bellinger's AI prompts

Modeling Conway's Game of Life (and all its variant rulesets) from scratch. I did this all on my own. The only references I used were to figure out the rulesets, their names, and the terminology.

Causal loop diagram based on my Gemini interaction Feb 2026 around Richard Soutwell's video Category Theory For Beginners: All Concepts, using Gene Bellinger's AI prompts

WIP Detailed unfolding summary of diagrams in Zalamea's 2022 article  Peirce and Grothendieck on Mathematical Cognition: A Merging of the Pragmaticist Maxim and Topos Theory

Overview of David Jaz Myers 2023 Book Categorical systems theory based on my March2026 Gemini interaction using Gene Bellinger's AI prompts See more applied category theory simple health examples insight

Modeling Conway's Game of Life (and all its variant rulesets) from scratch. I did this all on my own. The only references I used were to figure out the rulesets, their names, and the terminology.

The Logistic Map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popularized in a seminal 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation first created by Pierre François Verhulst. 

Mathematically, the logistic map is written

where:

 is a number between zero and one, and represents the ratio of existing population to the maximum possible population at year n, and hence x0 represents the initial ratio of population to max. population (at year 0)r is a positive number, and represents a combined rate for reproduction and starvation.
For approximate Continuous Behavior set 'R Base' to a small number like 0.125To generate a bifurcation diagram, set 'r base' to 2 and 'r ramp' to 1
To demonstrate sensitivity to initial conditions, try two runs with 'r base' set to 3 and 'Initial X' of 0.5 and 0.501, then look at first ~20 time steps

The Logistic Map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popularized in a seminal 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation first created by Pierre François Verhulst. 

Mathematically, the logistic map is written

where:

 is a number between zero and one, and represents the ratio of existing population to the maximum possible population at year n, and hence x0 represents the initial ratio of population to max. population (at year 0)r is a positive number, and represents a combined rate for reproduction and starvation.
For approximate Continuous Behavior set 'R Base' to a small number like 0.125To generate a bifurcation diagram, set 'r base' to 2 and 'r ramp' to 1
To demonstrate sensitivity to initial conditions, try two runs with 'r base' set to 3 and 'Initial X' of 0.5 and 0.501, then look at first ~20 time steps

Causal loop summary of Grothendieck's method of progress and bottlenecks in mathematics and his category theory concepts of topos and schema, based on my gemini interaction using  Gene Bellinger's AI prompts