The circuit described here is a chaotic version of a conventional phase shift oscillator. The nice thing about it is that it is simple and cheap. In addition, it operates from a single supply voltage and none of the component values are especially critical. Without the components inside the dashed outline, the circuit oscillates stably with a distorted sine-wave signal on the collector of T1. The three RC networks produce a net phase shift of 180 degrees at the operating frequency, which combines with the phase shift (signal inversion) of transistor T1 to maintain oscillation.
Adding the components inside the dashed outline results in a quite different situation. The amplitude rises while the oscillator is starting up, and at a certain level, this causes T2 to go into conduction. This, in turn, causes resistor R6 to be included in the feedback path, which disturbs the phase relationship and forces the circuit to try to find a different stable operating point.
Under the right conditions, this can lead to a chaotic operation, in which the circuit does not reach a stable state but instead passes through a succession of closely spaced unstable states. These paths form what is called an ‘attractor’, which can be readily displayed on an oscilloscope operating in X/Y mode with the following settings:
Channel 1: X, AC, 0.5 V/div
Channel 2: Y, AC, 20 mV/d
VCC: 6 to 16 V
By playing with the setting of potentiometer P1 and the value of the supply voltage, you can force the circuit to depart from stable oscillation and enter chaotic mode at half the previous frequency. This causes very interesting patterns on the oscilloscope (see photo). You can strongly influence the shape of the attractor by adjusting the values of P1, R6, C5 and the supply voltage.
The circuit has four components that are able to store energy, which makes its phase space four-dimensional. What you see on the oscilloscope screen is a two-dimensional projection of an attractor in four-dimensional phase space. Other dimensions can be made visible by connecting the probes to other points, such as Y and Z instead of X and Y.