Actually, the "aperiodic mode of oscillation" is a contentious issue, as imo use of the term is really a misnomer in this case. It would more aptly be called a "quasi-aperiodic mode" of oscillation, or QAM oscillation for short. I have obtained this QAM oscillation in my own testing of the circuit, and it is purely attributed to the non-periodic re-triggering of the 555 timer circuit used to drive the MOSFET. The resulting wave form output has a non-periodic component, but I would not classify it as chaotic.
The 555 can be configured as a crude voltage controlled oscillator (VCO) and the signals on pins 4, 5, and 6 will influence its timing parameters. Without going into a great deal of analysis, the gist of what occurs is that voltage transients on the 555-3 (output) and ground reference couple into the 555 circuitry and cause not only re-triggering of the output wave form at pin 3, but it can be adjusted to do so in such a manner that resembles the output of a swept VCO. The resulting pulse train is a pattern of between 2 to 6 pulses, each one with a decreasing pulse width and off-time between pulses, then the pattern repeats (i.e it is periodic). The very same result could be achieved by sweeping a 555 VCO circuit with a saw-tooth control voltage of appropriate amplitude and frequency
In any event, the switching wave form produced by this QAM oscillation being periodic, can easily be sampled and quantified using standard data acquisition at the appropriate sampling rate.
It should be noted however, that my observations are that the AT's data was not acquired with the circuit operating in the QAM oscillation mode. This can be easily verified by studying the wave forms as posted at EF.