Chua's Chaos Circuit

Introduction: Chua's Chaos Circuit

About: I'm a researcher who wants to make experimenting with chaos accessible to everyone. You don't need to be a rocket scientist to dabble in rocket science, same for chaos! I also like hackathons, and projects th…

**Note: This Instructable is based on parts from RadioShack, which is no longer in business. We encourage fellow makers to provide alternatives. This is the RAW Bill of Materials. We have written this academic paper on making the Chua's circuit out of parts from Fry's Electronics.**

This Instructable shows you how to build a chaotic circuit using parts from RadioShack, a widespread hobby electronics store in the USA. The only part RadioShack does not provide is an oscilloscope, but those are expensive anyway. Hence, we'll also show how you can use a USB Audio Adapter or a Desktop soundcard as an oscilloscope (or as we call it, the Poorman's scope).

It allows you to build a Chua's circuit with parts locally accessible in a short period of time without dealing with online shipping.

Chua's circuits are some of the simplest kinds of chaotic circuits. They are considered to be a classic example of true chaos due to their design and output. Using an oscilloscope you can witness a Chua's circuit create the strange attractor known as the double scroll. These beautiful patterns are truly chaotic and can be modeled by relatively simple nonlinear equations.
On top of being a great example of chaos, they are easy to build. These circuits, invented by Leon Chua, also have many real-world uses ranging from research, to music and encryption. In fact, customized circuits can be implemented almost anywhere where real chaos or nonlinear output is necessary.

You'll be able to have a chaotic attractor in the palm of your hands in just one day, be it for a hackathon, class demonstration, research, or personal curiosity.

Step 1: Go Shopping

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RadioShack stores differ from location to location. Some are entirely focused on consumer electronics and have very few items for hobbyists. Know which RadioShacks in your neighborhood actually have component drawers in the back. (Here in Downtown Brooklyn, 457 Fulton Street – Bad, Court St – Good, Atlantic Ave – Better).

Even if your RadioShack does have drawers in the back be prepared to improvise or visit a couple of places. Below are tables, parts, and other equipment-all available at RadioShack-that will allow you to put together and view the output of your Chua’s circuit without fancy equipment.

Basics Components*

#DescriptionStoreSKUQty.
1Duracell 9-Volt Battery Two Pack*N/A1
29V Snap Connectors (5 PCK)270-324, 270-3251
3Linear-Taper Potentiometer (10k or 5k)271-1715, 271-17142
4Resistors (500-Piece Value Pack)271-0031
5TL082 (8-PIN DIP)TL082/TL082CP4 (2 + 2 extra)
60.01uF 10% Film Capacitor272-1065, 272-10511
70.1uF 10% Film Capacitor272-1069, 272-10531
8DPDT Toggle Switch275-666 or any other DPDT switch1
920 Assorted LEDs276-1622**1

Note*: If you want the raw BOM (Bill-of-Materials) instead of a RadioShack shopping list click here.

Note**: It is my personal recommendation to use brand name 9V batteries such as Duracell. RadioShack has it’s own brand of batteries that gave me trouble in the past.

Note***: We only need two LEDs for this project. They come in two per package under the following SKUs: 276-021, 276-209, 276-022. I recommend the 20 pack because it's a bargain in comparison and the LEDs will fry if you hook them up wrong, hence having extras is always good.

Tools and Materials

#DescriptionStoreSKUQty.
iHookup Wire (22AWG Solid)278-12211
iiSolderless Breadboard Jumper Wire Kit276­-1731
iiiBreadboard276WBU202 or any other breadboard1
ivWire Stripper/Cutter6400223, 6400224*, 64002251
vMini Long-nose Pliers64000621
vi­5-Piece Basic Soldering Set**
(not in figure)
64­-28021
vii­Rosin Core Solder (2.5 Oz.)
(not in figure)
64­-0051

Note*: Best option.

Note**: This project does not require any precision soldering. The simplest/cheapest iron will suffice. I’ll be using my Weller WESD51 Digital Soldering Station.

Oscilloscope/Poorman's Scope

To see the chaotic attractor you need an oscilloscope, and we can make a cheap one with these parts...

#DescriptionStoreSKUQty.
A3 Ft. Stereo Patch Cable, Dual-RCA Plugs to Dual-RCA PlugsRCA*1
B14" (35.3CM) Insulated Test/Jumper Leads278-11561
CBEHRINGER U-CONTROL UCA222**UCA2221
C1 Mega-ohm Resistor271-1356
***
1

Note*: You can get the same RCA cables at your local dollar store as well.

Note**: You can get a UCA222 online, however any USB Audio Adapters that has a stereo input will work. Some are sold in music instrument stores such as Sam Ash.

Note***:This resistor is actually in the bag of 500 resistors listed in the first table

Step 2: Create Breadboard Switch

RadioShack does not have any DPDT (double-pole, double-through) switches that can fit into a breadboard. We'll use panel-mount DPDT switches and solder 22AWG wires to them instead.

  1. Cut 3 pieces of 1.5" (4cm) red 22AWG wire.
  2. Cut 3 pieces of 1.5" (4cm) black 22AWG wire.
  3. Use the wire stripper to strip the tips, and hook the wires to the DPDT switch connectors as shown in the images above. One side is for +9V (red), and the other for -9V (black). Use the pliers to help.
  4. Solder the wires to the switch connectors as shown in Figures 3 and 4.
  5. Use the wire stripper to strip the ends of the wires to have about 8mm (1/4") exposed. (See Figure 5)

  6. Plug the switch into the breadboard. Do all the connectors reach into the board? Can you flip the switch without it falling out? (See Figure 1)

You may realize that it is not necessary to solder on all six connectors for the circuit to work, but I strongly recommend doing so for structural integrity.

Step 3: Assemble -9V GND 9V Source

Here you will put together the circuit that connects the 9V batteries to the rest of the board. We use LEDs to help indicate that the batteries are working and to remind us to turn the switch off when you're done.

Note that you need to use the 220 ohm resistors in series with the LEDs, or else too much current will flow through them and they will burn out.

Follow the the images above which provide a breadboard layout, schematics and pictures of the actual board. Use whichever image your most comfortable with to build the circuit.

Make sure to test that BOTH LEDs turn on. Note that LEDs won't work if you plug them in backwards.

Step 4: Solder Potentiometers

RadioShack does have 10k potentiometers that you can fit inside a breadboard. We don't use them because it's too hard to tune the chaotic circuit into a chaotic mode with such small potentiometers. We'll use these big ones primarily for dexterity.

Solder long wires on all three leads for both potentiometers. We will only use two leads, but use the third one for structural integrity. We will want the potentiometers to be as steady as possible when we tune them.

Step 5: Assemble Chaotic Circuit

Now it's time for the bulk of the work. Build the chaotic circuit.

1. Prepare all the components that you need before building the circuit as I did on the white paper in the image above.

To help you find them, here are the resistor values you will need with their color code:

100 ohm x1 R7 BrownBlackBrownGold

1k ohm x2 R8, R9 BrownBlackRedGold

220 ohm x2 R1, R2 RedRedBrownGold

2.2k ohm x2 R3,R11 RedRedRedGold

22k ohm x2 R4,R5 RedRedOrangeGold

3.3k ohm x2 R6,R12 OrangeOrangeRedGold

2. Turn the Switch OFF, make sure the LEDs are not on. Don't build the circuit while the power is connected.

3. Start building the circuit, in the images above your are provided the breadboard layout, schematic and photographs of the circuit.

4. Check that you built the circuit correctly

5. Check that you built the circuit correctly

6. Check that you built the circuit correctly

7. Turn the switch ON.

Check that the LEDs go on as they should.

Feel if the 9V batteries are not too hot.

Feel that the ICs are not too hot.

If the batteries or the IC is hot, you will probably need to replace them.

Next part is to view the chaotic attractor on the screen. If you have an oscilloscope skip to Step 7.

Step 6: Poorman's Scope

If you have an oscilloscope skip this step.

The Poorman's Scope is a great replacement for an oscilloscope in many situations. The bulk of the work in this step is to make probes that will fit into the RCA slots of the USB Sound Adapter.

The software we use to see the chaotic attractor is called Soundcard Oscilloscope and the latest version can be found here.

1. Grab an RCA cable and snip off the tip of one end.

2. Look inside. As you can see there is a conductive wire in the center, and conductive wire along a circle around it.

The inner conductive wire holds the signal, and the outer is ground. We will access both.

3. Cut the outer casing about 1/2" (1.27cm) along the wire, but not deep. Just deep enough for you to bend the outer casing off. Get the ground conductive strands out of the way, and cut again to get to the strands at the inner core. NOT TOO DEEP, you don't want to cut the strands.

4. Go down another 1/2" (1.27cm) and this time only remove the outer casing. You should now have access to both the inner and outer strands. Make sure they don't touch! Cut the ground strands short enough that they won't touch the bottom of the signal strands.

5. Do this again for the other RCA cable.

6. Connect the green alligator clips to the ground strand. Green is ground by convention!

7. Connect the RCA plug into the INPUT of the USB Soundcard Adapter.

And you're done! You just made a Poorman's Scope.

Making the probe can take a bit of practice. You can get the same RCA cables at a dollar store, and keep cutting till you get it right.

Step 7: Enjoy Chaos

The videos below explain how to view the circuit output, either in a standard Oscilloscope, or with the Poorman Scope from the previous step.

Oscilloscope:

Connect the circuit to the oscilloscope. If you have a real oscilloscope, just connect the probes to capacitors C1 and C2.

Poorman's Scope:

If your using a Poorman's Scope, connect to C1 and C2 using the alligator clips with a 1Mega ohm resistor in between.

1Mohm resistors are: BrownBlackGreenGold

Tune the potentiometers slowly.

Enjoy!

For more details on Chua's circuits in general check out www.chuacircuits.com

Valentin Siderskiy and Richard Kroon

1 Person Made This Project!

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22 Comments

0
pfred2
pfred2

6 years ago on Introduction

I saved the schematic. I will have to build one of these someday. I have all of the parts kicking around already so that saves me a trip to the Shack.

0
vsiderskiy
vsiderskiy

Reply 6 years ago on Introduction

Great! Excited to see the results when your done.

0
kfjwheeler
kfjwheeler

Question 11 months ago

I notice that I have to dial the potentiometers very precisely to get chaotic behavior.

Is there any modification I can do to the circuit to make chaotic behavior easier to achieve or more stable?

0
vsiderskiy
vsiderskiy

Answer 11 months ago

Yes.

1. You can offset the potentiometer resistance with a resistor, and use a smaller potentiometer to get more dexterity (range per angular position). Or use a multi-turn pot.

2. Stable power supply is very important

3. If you design a PCB it works very well.

0
Abbas88
Abbas88

Question 1 year ago on Step 7

Hi Valentin,
Thank you very much for this amazing blog. I made this circuit and its working great!. However, I have a question: How can I see current signal (current through inductor) on oscilloscope?. I am not sure, But maybe we could place a shunt resistor(1ohm) in series with the gyrator circuit and measure the voltage across it?!. or there is a better way to do that ?
Thank you very much,
Abbas

0
Abbas88
Abbas88

Reply 1 year ago

HI Valentin,
Yes I have been thru that equation. I want to observe the pattern of inductor current and Vc1 and Vc2. For that I would need to see inductor current on the oscilloscope, how can I achieve it?

0
vsiderskiy
vsiderskiy

Reply 1 year ago

I see, you want to see it on the scope. You'll need an analog subtractor circuit to do the equation for you:

https://www.electronics-tutorial.net/analog-integr...

If you lose chaos, add two voltage followers in between the Chua's circuit and the subtractor circuit to isolate the two circuits.

https://commons.wikimedia.org/wiki/File:Opampvoltagefollower.svg

I know a shunt resistor sounds simple, but it won't work well because this uses a gyrator.

The other way to do this is get a smarter scope. I had one that inverts the signal and adds two signals together giving me VP-Y.

0
Abbas88
Abbas88

Reply 1 year ago

Thanks Vsiderskiy, this is very helpful!

0
RaviA43
RaviA43

3 years ago

can I know which circuit diagram you have used

0
vsiderskiy
vsiderskiy

Reply 1 year ago

Sure, it's in one of the images but hard to find:

0
kfjwheeler
kfjwheeler

Question 1 year ago on Step 7

How did you determine the voltage, resistor values, and capacitor values? What would happen if they were changed?

0
vsiderskiy
vsiderskiy

Answer 1 year ago

Hey, sorry for the late reply. It wasn't me who designed the circuit, but Dr. Leon Chua back in the 80's. There is a way to scale the system such that the system will be slower or faster by changing the inductors and capacitors all at the same time. At you change values you may go out of exhibition of chaos and my have a steady state system (no change in voltages) or a simple oscilllator (sine waves).

0
cyanocyclohexane
cyanocyclohexane

2 years ago

Why are you using TWO TL082? I believe there are two little opamps in ONE TL082.

0
vsiderskiy
vsiderskiy

Reply 1 year ago

Yes you are correct we are using two TL082s. Two Op-Amps for the nonlinear resistor, and Two Op-Amps for the inductor-gyrator. Notice in my circulate I'm not using an inductor, but a circuit that emulates the inductor value that I need.

0
kfjwheeler
kfjwheeler

Reply 1 year ago

You need 4 op amps altogether.

0
Abbas88
Abbas88

1 year ago

I made it, and its working pretty awesome!

0
Abbas88
Abbas88

Reply 1 year ago

here is oscilloscope output (Vc1 Vs Vc2)

Screen Shot 2020-06-26 at 12.10.55 PM.pngScreen Shot 2020-06-26 at 12.10.34 PM.pngScreen Shot 2020-06-26 at 12.09.49 PM.png
0
vsiderskiy
vsiderskiy

Reply 1 year ago

Looks fantastic!!!