Chaos Computer

Chaos Illustrated by the Analog Computation of the Lorenz Equations

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This simple circuit has extremely complex, chaotic dynamics that are beautiful to watch, inspiring, and will hopefully be used by educators as a tool to interest students in science and engineering.

What is it?
The Chaos Computer is an analog computer that solves the Lorenz Equations to produce beautifully complex waveforms.

The computation of the three non-linear differential equations is performed entirely by analog electronic components; there is no digital computer on the board at all! The circuit is based on the well known implementation by Paul Horowitz with added functionality for easy user interaction.

Check out this brief video showing the Chaos Computer in action!

What is Chaos Theory?

Chaos theory is the study of dynamic systems that are highly sensitive to initial conditions. This characteristic leads to seemingly random behavior, but in fact the dynamics are perfectly deterministic. There are many real world examples of chaos such as the weather, turbulence, the motion of a double pendulum, irregular heartbeats, and many more. The Wikipedia page on chaos theory has a lot of information if you're interested.

The quintessential chaotic waveform (shown in the image below) resembles a butterfly's wings, which led to the idea of the butterfly effect. I.e. Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?

Why did I make it?
There are plenty of mechanical devices used to entertain physicists, engineers, and enthusiasts as they contemplate the complexities of the universe. They can watch the balls of a Newton's Cradle exchange momentum, hear the energy being dissipated in an Euler Disk, feel the precession of a gyroscope, etc.

I've designed this Chaos Circuit as a tool to visualize a unique electrical system that is both beautiful and wildly complex. The purpose is to entertain, to provoke thought, to inspire, and to provide a glimpse into nature's complexity.

Who is it for?
For Electrical Engineering Enthusiasts

The Chaos Circuit is a basic analog computer similar to those used to solve complicated equations and models before the digital age. It's awesome to watch incredibly complex dynamics being actively generated by common electrical components. If you're anything like me, you'll find yourself staring at the chaotic waveforms on your oscilloscope while contemplating life and the impact that all of your choices have on the world.

For Educators
Inspiring your students is a priority whether you're teaching high school physics, undergrad engineering, or graduate level mathematics. This circuit illustrates beautiful complexity in nature, coupled with digestible mathematics and simple circuit design. Watching the chaotic output is enough to inspire a student, but you can also dive deeper into the physics and mathematics for more detailed lessons/research.

For Researchers
If anyone has a need for a chaotic output for research purposes, please let me know. I'd be very interested to hearing what you have planned and I'd be happy to help out if I can by modifying the design!

Technical Info
All three outputs of the Lorenz equations (X, Y, and Z) are made available on the circuit (accessed by the test points) so that you can explore all of the waveforms. There are three switches on the board that should all be set to the same value in order to control the time constant of the circuit, which allows the user to slow down the output waveforms for visualization purposes (see video). There are also two potentiometers that are used to control two of the three initial conditions (β and ρ).

The Chaos Computer requires 18 VDC to 30 VDC, and ~15 mA to properly operate. Please note that an isolated power supply should be used to supply power to the Chaos Computer (power supply ground not continuous with Earth ground). This is because the GND on the circuit board is virtual and many oscilloscopes connect the ground probes directly to Earth ground. Using a non-isolated power supply would cause a potentially damaging short that would cause the circuit to malfunction. Reversing the input polarity to the circuit will damage the circuit as well.

  • 3 × 2000 pF cap
  • 3 × 0.1 uF cap
  • 8 × 0.47 uF cap
  • 12 × 10k resistor
  • 2 × 100k resistor

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  • Chua's Circuit

    Tom Quartararo03/22/2016 at 17:33 0 comments

    I've made a version of the popular Chua's Circuit in an effort to reduce the cost of having a circuit that illustrates chaotic dynamics. The lack of expensive analog multipliers and removing the ability to modify the circuit's time constant allowed for a much reduced cost in comparison to the analog computation of the Lorenz equations computer. Stay tuned.

  • Goals

    Tom Quartararo02/16/2016 at 12:51 0 comments

    Hello everyone!

    I'm planning to release some documentation soon that explains the circuit and mathematics to the best of my ability. The goal is to develop a lesson plan that can be used to explain the device simply and effectively in an effort to interest people in science and engineering.

View all 2 project logs

Enjoy this project?



cuestore296 wrote 08/11/2019 at 11:48 point

Seguí las instrucciones y no funciona. Solo salen puntos aleatorios en la pantalla del osciloscopio. Ruego Cambio y / u operativa clara.

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cuestore296 wrote 08/10/2019 at 22:12 point

No funciona.

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Tom Quartararo wrote 08/13/2019 at 13:37 point

Problem solved! There was an issue with the oscilloscope settings

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rafa wrote 10/09/2017 at 01:25 point

Out of curiosity, how did you split the power rail?

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Susan wrote 04/29/2016 at 01:03 point

I was just going to ask the same thing.  Here is an older circuit I found online

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Evan Salazar wrote 04/28/2016 at 18:21 point

So Cool!, Do you have Schematics posted somewhere?

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Tom Quartararo wrote 04/29/2016 at 13:03 point

I based my circuit on the schematic linked by Susan, but I added in some potentiometers and switches to control the coefficients and time constant.

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toby wrote 10/23/2020 at 22:58 point

I designed my own based on the same Horowitz design, but while it worked on the breadboard, my OSHpark PCB has been much less reliable. I would certainly like to compare your actual schematic. Or if you are aware of any gotchas with time constant caps as small as 220pF, I'd love to hear! (worked on breadboard). I am using through-hole components, dual supplies and the MPY634 and LF412 chips that Horowitz originally did (added LM2904 buffers and an LM393 comparator).

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