Create distortion from basic linear (and non-linear if neccessary) DSP elements

I'm studying mechatronics and I'm intrested in DSP basics. My lecturer said that there are four basic linear DSP elements:

1. Adder (and other mathematical operations)
2. Amplification (shown on diagrams as triangle)
3. Delay ($z^{-1}$)
4. Junction

I know from electronics that I can create distortion using for example op-amps and clipping circuits - and I can do it practically. But is there a way to create distortion using four DSP elements theoretically? I know distortion is non-linear - so if not this four elements, what kind of elements existing in theoretically DSP should i use?

• Can you control the gain of the amplification by another signal? – Olli Niemitalo Mar 6 '17 at 17:22