chua_circuit_posts.txt

# Chua Circuit - Social Media Posts
# Generated by AGENT_PUBLICIST

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## SHORT-FORM POSTS
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### Twitter/X (< 280 chars)
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Chaos from just 5 components! The Chua circuit creates the famous double scroll attractor - a simple electronic circuit that produces genuinely unpredictable behavior. Tiny changes → wildly different outcomes.

#ChaoticSystems #Python #Electronics #NonlinearDynamics #Math

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### Bluesky (< 300 chars)
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The Chua circuit is the simplest electronic system exhibiting chaos. With just 2 capacitors, 1 inductor, 1 resistor, and a nonlinear diode, it generates the beautiful double scroll attractor. Our simulation shows how a 0.0001 change in initial conditions leads to completely different trajectories.

#Science #Chaos #Python

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### Threads (< 500 chars)
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Ever wonder what chaos looks like in electronics? The Chua circuit is literally the simplest possible circuit that can be chaotic.

It has just 5 components, but produces this wild double scroll attractor pattern. The coolest part? Change the starting voltage by just 0.0001 and you get a completely different outcome. That's the butterfly effect in action!

Built with Python using scipy's ODE solver. The bifurcation diagram shows exactly how the system transitions from order to chaos.

#Physics #Python #Math

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### Mastodon (< 500 chars)
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Simulated the Chua circuit - a canonical example of electronic chaos.

System equations:
dx/dτ = α[y - x - f(x)]
dy/dτ = x - y + z
dz/dτ = -βy

Where f(x) is the piecewise-linear Chua diode characteristic with slopes m₀ ≈ -8/7 and m₁ ≈ -5/7.

With α = 15.6, β = 28, the system produces the double scroll attractor. Estimated largest Lyapunov exponent λ₁ ≈ 0.3 confirms chaotic dynamics. A perturbation of 10⁻⁴ amplifies by ~1000x over τ = 50.

#NonlinearDynamics #Chaos #Python #SciPy

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## LONG-FORM POSTS
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### Reddit (r/learnpython or r/science)
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**Title:** Simulating Chaos: The Chua Circuit Double Scroll Attractor in Python

**Body:**

**What is the Chua Circuit?**

The Chua circuit, designed in 1983, is the simplest electronic circuit that exhibits chaotic behavior. It uses just 5 components: 2 capacitors, 1 inductor, 1 resistor, and a special nonlinear element called Chua's diode.

**Why does it matter?**

It's become the "fruit fly" of chaos research - simple enough to study, yet rich enough to show all the hallmarks of chaotic systems:
- Strange attractors
- Sensitive dependence on initial conditions
- Period-doubling route to chaos

**The Math (simplified)**

The system is described by three coupled differential equations. In dimensionless form:

dx/dτ = α[y - x - f(x)]
dy/dτ = x - y + z
dz/dτ = -βy

The nonlinearity f(x) is a piecewise-linear function that acts like a negative resistance in certain voltage ranges.

**What I learned:**

1. **Sensitivity is real** - Changing initial x from 0.7 to 0.7001 (0.01% difference) leads to trajectories that diverge by 1000x after just τ = 50

2. **Bifurcation diagrams are beautiful** - As you vary α from 8 to 16, you can see the system go from periodic orbits → period doubling → full chaos

3. **Lyapunov exponents quantify chaos** - A positive largest Lyapunov exponent (≈ 0.3 for standard parameters) mathematically confirms exponential divergence

**Code highlights:**

Used `scipy.integrate.solve_ivp` with RK45 method and tight tolerances (rtol=10⁻⁸) to accurately capture the chaotic dynamics. The piecewise Chua diode function uses absolute values for a vectorized implementation.

**View the full notebook with interactive code:**
https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/notebooks/published/chua_circuit.ipynb

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### Facebook (< 500 chars)
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This is what chaos looks like! The Chua circuit is the simplest electronic circuit that produces genuinely unpredictable behavior - just 5 basic components creating this mesmerizing double scroll pattern.

The wildest part? If you change the starting conditions by just 0.01%, you get a completely different outcome. That's the butterfly effect, and this circuit demonstrates it perfectly.

Explore the full simulation: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/notebooks/published/chua_circuit.ipynb

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### LinkedIn (< 1000 chars)
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Computational Modeling of Chaotic Systems: The Chua Circuit

I recently completed a numerical simulation of the Chua circuit - a canonical example of deterministic chaos in electronic systems.

Key Technical Aspects:
• Implemented the three coupled ODEs governing circuit dynamics
• Used scipy's solve_ivp with adaptive RK45 method and high-precision tolerances (rtol=10⁻⁸, atol=10⁻¹⁰)
• Generated bifurcation diagrams showing the period-doubling route to chaos
• Estimated the largest Lyapunov exponent (λ₁ ≈ 0.3) to quantify chaotic dynamics

Skills Demonstrated:
• Numerical integration of stiff nonlinear ODEs
• Scientific visualization with matplotlib (3D phase portraits, projections, bifurcation diagrams)
• Analysis of dynamical systems (fixed points, stability, Lyapunov exponents)

The simulation reveals how a perturbation of just 10⁻⁴ in initial conditions amplifies by three orders of magnitude, demonstrating the practical implications of sensitive dependence in control systems.

View the complete Jupyter notebook: https://cocalc.com/github/Ok-landscape/computational-pipeline/blob/main/notebooks/published/chua_circuit.ipynb

#Python #ScientificComputing #NonlinearDynamics #DataScience #Simulation

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### Instagram (< 500 chars)
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The simplest chaos machine

This is the double scroll attractor from a Chua circuit - just 5 electronic components creating pure mathematical chaos.

What you're seeing is a system that's completely deterministic (no randomness!) yet impossible to predict long-term.

Change the starting point by 0.01%?
Completely different outcome.

That's the butterfly effect, visualized.

Simulated with Python + SciPy
50,000 time steps
High-precision numerical integration

The beauty of nonlinear dynamics in one image.

#chaos #physics #mathematics #python #dataviz #science #electronics #nonlineardynamics #strangeattractor #visualization

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