Consider the response time of VOMs which is better at viewing the smooth dynamic changes than using rapidly changing DMM.
When the resonant frequencies are chosen in the range of 1Hz, or RC values in the 3 second range, one can see that the Chaotic Gyrator Oscillator also has a aside circuit which is analog flip flop from positive feedback that changes the resonant frequency by alternating the gyrator’ RC time constant slightly and at the same time the mean voltage toggles between two levels of this Oscillator in each “quasi-synchronous” state. This gives the random chaos figure 8 patterns and other Lissajeau XY scope figures that characterize this design. The VOM would see an oscillating sine shift between two mean levels determined by some astable circuit thresholds on the other side.
Since the bistable side is analog and quasi-synchronous its effect is continually changing the initial conditions for stable oscillation at f1 and f2 while affecting the mean voltage for each. This results in no identical patterns in a short time span, but over a long time span, the patterns may become obvious by the min/max range limits and cycle times of each longer pattern. Changing the R ratios or discrete values also affects these patterns greatly as well as the resonant frequencies of the gyrator Oscillator when appropriately tuned. So there is a sweet spot for maximal gyrations or wobbles.
There is an excellent circuit simulation of this on the Falstad website if you look under the circuit menu for other circuits near the bottom.