The circuit:
The core is a 20M generating random numbers, and then using those numbers to advance or decrease the count.
To assist in the randomness, the AC waveform is sampled via the ADC10 command, and its value is used as a "seed" in the random variable.
The Nixies operate from 170VDC, and the Dekatron require 510VDC. To obtain those voltages, a small 12VDC to 170VDC module provides a safe method to do so.
https://threeneurons.wordpress.com/nixie-power-supply/
The 170VDC comes straight from the module, the 510VDC utilizes a voltage tripler, as outlined in the same website.
The easiest way to drive a Nixie is utilize the 74141 IC. It requires a TTL level BCD input, and decodes the 10 segments with a high voltage driver.
The Dekatron requires a two phase drive, similar to stepper motors, for rotation and direction control. The Dekatron also features an"index" pin, really a zero count detector, to synchronize it.
I included some sound effects, which are timed with the Dekatron counting pulses. Simultaneously, the Neon lamps are pulsed.
Although I could have used a single Picaxe to drive both Dekatrons and Nixies, I decided to utilize wo independent devices to enhance the randomness.
Lastly, to increase the entropy, both Picaxes tickle each other via the sync pin.