How to wire potentiometer from Arduino

I have a few projects, like this Atari punk console, for example - uses potentiometers and 556 timer chip to make sound effects (which is a fun project, btw).

Wikipedia diagram for Atari punk console - 556 timer

I would like to control the potentiometers through Arduino some way. I know it's only digital output signals, so I need to learn something a little complex, I predict. Can someone give me some links, advice so I can look up and learn how to do this, please?

You can use a digital potentiometer controlled by the Arduino. Be careful, as the output side is not isolated from the Arduino. You can’t control a 12V circuit with it.

Or a PWM output can be smoothed to make an analog voltage output.

Or a Due or a Teensy can be used, for the direct analog output, which also has some limitations, particuarly on the Due.

You can get motor-driven potentiometers too, if you need to see the knob turning.

Morgans: Thank you for the reply. The digital potentiometer is a good idea. It's interesting, and will solve the issue of that filthy noise interference I seem to get when turning the pots. I'm familiar with opto isolation chips, so I will explore this option.

Regarding the pwm output, and smoothing. Would this be digital / analog conversion? Unfortunately, I do not own or know how to use an oscillioscope yet, so I can't get a good clear understanding of what type of signal, voltage and current is running through the circuit I'm trying to manipulate. I am still getting headaches studying the math needed to divide resistors, using capacitors - which wouldn't matter anyway since I have no scope to test my work. I wish I could find a useful oscilloscope I could afford.

I haven't used a Teensy or Due yet, they are on my list of things to buy & try.

First question, what is the supply voltage in that Atari punk console circuit? If its not the same 5V as the Arduino you will need to think about level shifting and so forth.

If you do the calculations correctly then you don't need a scope for this simple circuit. There's lots of online calculators available.

Although it is really nice to see the results of your work. Since the output signal is well-known, you can easily use a resistor divider to get it back within the 0-5V analogRead range of the Arduino, perhaps you can use a second Arduino to read the output and print it to the serial monitor. Unacceptable ripple in the D-A conversion will show up as random numbers in your output.