In mathematics, a Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous figure or Bowditch curve /ˈbaʊdɪtʃ/, is the graph of a system of parametric equations{\displaystyle x=A\sin(at+\delta ),\quad y=B\sin(bt),}

which describe complex harmonic motion. This family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail by Jules Antoine Lissajous in 1857.

A Fourier series is a way to expand a periodic function in terms of sines and cosines. The Fourier series is named after Joseph Fourier, who introduced the series as he solved for a mathematical way to describe how heat transfers in a metal plate.

The GIFs above show the 8-term Fourier series approximations of the square wave and the sawtooth wave.

h=v_ox*t-g*t^2/2

THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION

The existing global capitalistic growth paradigm is totally flawed

Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a component the creation of unpredictable chaotic turbulence puts the controls ito a situation that will never return the system to its initial conditions as it is STIC system (Lorenz)

The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite working containers (villages communities)

THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION

The existing global capitalistic growth paradigm is totally flawed

Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a component the creation of unpredictable chaotic turbulence puts the controls ito a situation that will never return the system to its initial conditions as it is STIC system (Lorenz)

The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite working containers (villages communities)

Revisited Conceptual map (Directed Cyclic Graph) of Applied Category Theory as practised by Osgood, Rosiak, Spivak and Baez, based on my Apr 2026 Gemini interaction using Gene Bellinger's AI prompts

Causal loop diagram summary based on Richard Southwell's video Category Theory For Beginners: Open Dynamical Systems and my Gemini interaction Feb2026 using Gene Bellinger's AI prompts

Contrôle position angulaire d'un moteur électrique (aimants permanents)

THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION

The existing global capitalistic growth paradigm is totally flawed

Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a component the creation of unpredictable chaotic turbulence puts the controls ito a situation that will never return the system to its initial conditions as it is STIC system (Lorenz)

The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite working containers (villages communities)

In mathematics, the Fibonacci Sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci Numbers, commonly denoted Fn . The ratio of two consecutive Fibonacci numbers tends to the Golden Ratio as n increases.

Feb2026 summary concept map with loops (Directed Cyclic Graph) of Gemini interaction about Sheaf theory and its relationship with other Category Theory using Gene Bellinger's AI prompts Revisited interaction April  2026 based on Daniel Rosiak's (free) book Sheaf theory with examples

Top-down Concept map based on Gemini interaction Feb 2026 using Gene Bellinger's AI prompts

Ce modèle 2D simule la mise en orbite d'une charge utile par un lanceur (Ariane 5) et donne les paramètres orbitaux de l'orbite atteinte.

Categorical systems theory applied to health services integration and surge response based on my March2026 Gemini interaction using Gene Bellinger's AI prompts. See more complete health service reliability insight based on emery roe's work

Conceptual structure (Directed Cyclic Graph) of the Yoneda lemma  based on Gemini interaction Feb2026 using Gene Bellinger's AI prompts

Conceptual map (Directed Cyclic Graph) of Applied Category Theory based on my Feb 2026 Gemini interaction using Gene Bellinger's AI prompts

THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION

The existing global capitalistic growth paradigm is totally flawed

Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a component the creation of unpredictable chaotic turbulence puts the controls ito a situation that will never return the system to its initial conditions as it is STIC system (Lorenz)

The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite working containers (villages communities)

Interaction with Gemini AI using Gene Bellinger's Prompts Jan2026 Focus on Eugenia Cheng's 2024 presentation Learning Category Theory

Causal loop summary of Colin McLarty's 2015 AMS  article  based on my gemini interaction April 2026 using Gene Bellinger's AI Prompts

WIP Fuller Causal loop summary of Zalamea's 2022 article Peirce and Grothendieck on Mathematical Cognition: A Merging of the Pragmaticist Maxim and Topos Theory

Categorical systems theory based on my March2026 Gemini interaction using Gene Bellinger's AI prompts See more applied category theory simple health examples insight