double scroll attractor on an analog scope
Double scroll attractor shown on an analog scope

double scroll attractor on a digital scope
Double scroll attractor shown on a digital scope

circuit board with double scroll attractors on two scopes
Circuit board with double scroll attractors on analog and digital scopes

double scroll attractor from matlab simulation
Double scroll attractor from Matlab simulation

lemon attractor
Lemon shape before the double scroll

saturated double scroll attractor
A saturated double scroll attractor caused by low voltage

Building Chua's Circuit

Evenutally you should come up with something like Figure A. This is the classic chaotic double-scroll attractor also known as Chua's attractor. This figure, however, comes from an analog scope–not a digital one. A digital scope will really not give quite the same effect, and it can be quite difficult to see if you have even gotten a double scroll or not. It basically looks like a bunch of dots, as in Figure B. Analog scopes are for some reason harder to come by these days, but they are invaluable when you are looking at these circuits.

You can try plotting the circuits with X vs Y, X vs Z and Y vs Z to see the scroll from different 2D perspectives. In a simulation you can actually rotate the attractor in 3D. Check out our simulation page to see the double scroll evolve much slower than you will be able to see on an oscilloscope. It will give you a feel for how the signals interact to actually create the double scroll attractor.

You can also view the circuit through a digital scope for comparison. Figure C shows a double scroll displayed on two scopes, one digital and one analog, using a custom-built Chua's circuit. Note the easy-to-adjust potentiometer knobs. This circuit is very easy to tune anyway, because it was custom fabricated with good components.

Figure D shows an ideal double scroll attractor generated from a Chua's circuit simulation in Matlab. Note that it is plotted in 3 dimensions, with X, Y and Z, while on your oscilloscope you will plot just two signals. The double scroll attactor is what you are looking for when building the circuit and indicates a truly chaotic system. Before you get the double scroll, you technically do not have chaos.

When you first set up your circuit and look at it in your oscilloscope, you may be getting wavy signals but when you plot the signals against each other (e.g. X vs Y) you may still only see a little squiggle, or worse, just a bright dot. To make the double scroll appear, you must manually adjust the two potentiometers (labeled R and R10 on the components page) until you get to just the right spots.

Where is the right spot? When it looks right. This part is more art then science and may take a bit of fiddling depending on the quality of the circuit you are dealing with. I mentioned before that on poorly built circuits, any small vibration may change the output.

The best advice I can give you when you are stuggling to find the double scroll, wildly tuning both pots with no luck, is to very slowly tune one at a time until you see a shape like in Figure E. Once you see this lemon shape, start tuning the other potentiometer, slowly again, until you get the double scroll. That usually works, so if you still have problems check your circuit again.

You may find that one side of the scroll is bigger than the other, as in these pictures. This is likely due to uneven voltages from the two power sources or improperly tuned parameters.

Another problem you may have is a saturated scroll, as shown in Figure F, where the scroll seems to be bounded on two sides and is flat instead of rounded. Saturation, or 'voltage clipping', is caused by voltage that exceeds the ideal funtional range of the component and reaches the limits of the components of the circuit.

'By definition, the Double Scroll attractor is bounded. This is important because all physical resistors are eventually passive, meaning simply that for a large enough voltage across its terminals, the power consumed by a real resistor is positive.' [Kennedy, Robust Op Amp Realization of Chua's Circuit, 1992]

If clipping occurs on the X variable, your C1 value is too small. Simply tuning the circuit or changing the capacitor to one compatable with the voltage you are dealing with will get rid of saturation. We have also modelled a saturated scroll in our our Matlab simulation, using a smaller value for the capacitor C1 and a larger value for the resistor R.

However, if clipping occurs on the Z variable, saturation may be caused by too small of a value for R10–in the inductor simulator.

On the circuit described here, it is possible to demonstrate saturation on a perfectly working circuit. R10 being a poteniometer makes it possible to tune the parameters to show a full double scroll or to go beyond this to demonstrate saturation.

When you finally get a double scroll attractor running, you can try using its signals (now officially chaotic) for your research, experiments or you can even try synchronizing two or more chua's circuits. For extra credit, you can modify the circuit and create three or more scrolls from a single circuit!