Electronics > Projects, Designs, and Technical Stuff

The Rössler attractor challenge.

**GK**:

Depending on the enthusiasm and interest of others out there, this thread may either flop or become a catalyst for a veritable flurry of highly exciting activity.

The challenge is to design and breadboard an functioning analog circuit to solve the three coupled differential equations of the Rössler attractor:

Those equations are taken from the Wikipedia page here: http://en.wikipedia.org/wiki/R%C3%B6ssler_attractor

The constants, a, b and c are subject to some variability, but a good place to start is a=0.2, b=0.2 and c=5.7.

The variables can be altered so long as the values chosen still result in a chaotic solution.

Now, being the amazingly clever person that I am, I have already worked out a circuit to do the job. Here it is:

At this stage I won't post the circuit diagram, as that would give most of the game away. However I will reveal that I simplified the initial solution down to six op-amp stages (one quad and one dual package) and one analog multiplier chip. Here is the resultant display:

Ultimately, it would be interesting to see how multiple independent workings of the design problem converge on the same outcome. So, at this stage, here is what I suggest for all those who may wish to take part:

1) Work out and breadboard your circuit

2) Post a photo of the resultant oscilloscope display and give your values for a, b and c.

3) Give your active device count (op-amps, etc) but do not reveal your circuit details or workings.

Only once enough players of the game have posted up their scope display photos as proofs off accomplishment can the circuits and workings be revealed. He or she who solves the problem with the simplest circuit wins!

However, you must build your circuit and demonstrate success with an oscilloscope display photo at a minimum!. SPICE results are not acceptable! There are minor challenges to getting a real life analogue solution up and running that to not present themselves in virtual reality; namely, I can reveal, the issue of scaling so that the solution falls withing the voltage swinging limits of the active circuitry and dealing with offset voltages.

Finally, on the topic of the scope display, unless you have a 3-dimensional projection unit like I have, you will need to build a simple circuit to give the Rössler Attractor, which is a 3 dimensional object represented by three-axes variables, perspective for a 2 axis XY oscilloscope display. Attached immediately below is the simple circuit required. It adds the X and Z solutions/signals in such a way as to give a 45 degree tilt to the projection along the horizontal axis, as shown. You do not have to build this circuit to demonstrate success of course, but your display of the attractor will not be as pretty as it may be otherwise as you will be restricted to viewing/displaying the attractor "end on" only, with a display generated by a selection of only two of the three axis variables at a time.

Have fun!

**kfitch42**:

Speaking of Chaotic electronics, have you ever tried Chua's Circuit? http://en.wikipedia.org/wiki/Chua%27s_circuit

That one has been on my todo list for a while... but given the fact that the inbound flux of my todo list is greater than the outbound flux... and the honeydo list having higher priority...

**Dajgoro**:

Could somebody explain what do exactly do this circuits do, and is there any propose for them?

**Paul Price**:

Rossler attractor equations are useful in modeling equilibrium in chemical reactions.

**GK**:

--- Quote from: kfitch42 on September 03, 2013, 05:06:51 pm ---Speaking of Chaotic electronics, have you ever tried Chua's Circuit? http://en.wikipedia.org/wiki/Chua%27s_circuit

--- End quote ---

Yep

--- Quote from: Dajgoro on September 03, 2013, 07:03:16 pm ---Could somebody explain what do exactly do this circuits do, and is there any propose for them?

--- End quote ---

Purdy squiggles on the oscilloscope.

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