Tuesday, June 16, 2015

The Aizawa attractor III

Here's my patching for the Aizawa attractor (see previous posts):


This uses all three multipliers, the divider (as a fourth multiplier), and the two squarers. The cubes are obtained directly using the (AD538 based) nth power circuits.


Amazingly, this all worked first time. Still sans oscilloscope - will be interested to see the attractor with the computer in FAST mode. In the meantime, here is the plotter output (1 µF integration capacitors). The plot shows the first ten minutes of the trajectory.

2 V/cm both axes, 10 minutes' worth of trajectory.

Pleasingly, this agrees pretty well with other published images of the Aizawa attractor e.g. [1], although the latter appears to be an inverted mirror image of what I produced - perhaps the axes in [1] are reversed. The image of the attractor given in [2] does have the same handedness as mine.

Clearly, the attractor has some degree of symmetry about the z-axis. In the previous posts, I deduced that the attractor has three equilibrium points, lying along the z-axis:


Now, the first one (z = 1.9432644 V) does appear to correspond to the top of the attractor. But, the other two are well below the attractor. The bottom of the attractor is at about -0.58 V. This discrepancy requires some thought...


Reference

[1] http://www.algosome.com/articles/images/aizawa-attractor.jpg

[2] http://i.imgur.com/wMrmY.jpg

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