EMS inspired designs VCS3, Synthi, and friends
• This isn't exactly a eurorack clone, but they are patches that simulate a specific family of hardware made by EMS in the 1960's and 70's which are just as much touchstones for musical circuit design as Moog and Buchla's.

https://en.wikipedia.org/wiki/Electronic_Music_Studios
• As @Rudiger pointed out in this link, the EMS oscillators were able to create parabola type waveforms using a waveshaper circuit.

Here are some screenshots of the oscilloscope looking at the sine wave and rectified sine wave on the iVCS3 app.
• Here is my first pass at making something to match the waveforms displayed. My impression is that the sinusoid is probably a diode clipped triangle wave like the Noise Reap Bermuda oscillator as you can still see the peak of the triangle wave. I have no idea how the wave rectifier worked so it's just my best guess.
• So I did a another version. This time I made no attempt to model the vcs3's imperfections and tried to make a smooth crossfade from a negative rectified sine wave through a sine wave into a positive rectified sine wave. There is a pulse wave output for syncing these in a chain of phase or frequency modulation, with attenuators to the incoming signal built in. There is a sub oscillator signal that I made great efforts to track the zero crossing so when multiplies with the sine output it created as few edges in the waveform as possible. It isn't perfect, but it gives the wave some overtones without going totally square wave in timbre.
• For fun I built a simple parabolic wavetable to see how it would sound. Actually sounds pretty good. If you look at the waveform at low frequencies, you'll see what looks like a DC offset of some kind. When I do the FFT, I notice a very strong DC offset, not quite as strong as the fundamental, but definitely stronger than the first and subsequent harmonics. I suppose that's because the function is fundamentally not sinusoidal, but I don't know. The actual content of each wave table is the output of an inverse FFT, which I think is what brings the DC offset back into the picture.
• Of course, that's equivalent to the following: http://take.ms/QljJ0 (though this one aliases).

I suppose having a "pure" parabola isn't the point. :)
• @jjthrash The parabola is a pretty nice waveform, like the ramp/saw wave it has all the harmonics but is far more mellow, analogous to how the triangle has similar harmonics to the square wave but is more mellow. Underutilized IMO!