I approach Eurorack much like a regular hardware synth. Make some bass sounds, leads, modulated fx sounds. I use a DAW when I write or am working on ideas. I capture any melodic ideas in MIDI as they come, which I can then run thru synths and effects to experiment. However, I want to incorporate some randomisation and see where some generative melody experimentation can take me, even if I want to stay within key or the particular "mode", music theory wise.

I have looked at the following:
- 2HP Rdm, followed by a 2hp Tune (quantizer) seems like a bare bones way to do this.
- The Music Thing Modular Turing Machine seems to have a little more functionality, though it would still need a quantizer (I believe). I like that it can vary its randomness over time, and you can freeze or lock a pattern. Seems user friendly.
- The Ornament and Crime seems like it can do what the above do, plus a million other things (which is why it seems a bit daunting to just dive into). Trying to even read and understand what exactly the O&C actually DOES is intimidating.

Any other options I should consider? Size / cost / functionality all matter, but being intuitive to use seems pretty important too. I know it if it is super complex, I am just going to struggle with it versus get inspired.

Randomization doesn't equal generative, per se. It's a part of it, to generate variation, but you can't make up a decent generative structure out of pure randomness.

A better idea, and this actually would be generative:

-Take a series of LFOs. Four of these feed modally-set quantizers and cycle through their waveforms at slightly different periods. -Now, feed these four LFOs with differently-timed quadrature LFO signals, so that one of each pair of the first LFOs is offset by 90 degrees phase from the other.
-Next, feed these two quadrature LFOs with a single master LFO at a very low rate of change. Also, one of those feeds should go through a CV-able polarizer, which is being controlled by one of the quadrature LFOs (reverse-feedback control structure, more or less).
-Now, add comparators. These step the quantizers, and also provide trigger/gates for VCAs, VCFs, down the line, in the voice structure. We'll just deal with the control structure here, tho. Each comparator is paralleled to the initial LFO outputs via mults, but each one's trig/gate output affects a different voice than the originating LFO/quantizer pair controls the pitch of.
-Patch each of the quantizer outputs to a VCO in the voice chain, and then keep patching as normal for voicing.

Notice that, while the summed behavior of the output pitches is also, in a sense, random...it's actually not. Instead, what you hear is the result of a rather complex algorithm of voltage curves, smoothed into pitches through the use of quantizing. But given that there are constraints present in the various LFO rates and waveforms, the comparator settings, the quantizer modalities, the VCO tunings that allow each of these a randomness within a range of N actions (N being the factor of constraint created by the settings as well as control inputs), it's technically NOT random. Instead, the result is generative...a constantly-spun pattern of notes in four-voice polyphony, non-repeating, but constrained in such a way that there is a seeming predictability to the result, despite the fact that there is no actual proper 'control' applied. A better way to think of it is to look at it as a 'chaotic' process; not random, but certainly not linear, either.

Good points, and an interesting patch idea.... for much further down the road. I might be using the word "generative" in its most generic or basic way, versus a much deeper definition that modular guys would, and maybe there is a better word to carry my point. Creating a big self-playing patch that evolves over time might be a real "stretch goal", but the more immediate goal is to break away from meticulously writing / sequencing everything and inject some randomness.

It can be an interesting goal, though. I've done generative-type patches on some not-too-huge systems that involved less internal variation, but which used external processing variations to create all of the complexity. The key thing to remember is that your 'instrument' in electronic music isn't limited to the particular boxes in question, but is in fact made up of everything you've interconnected. Hence the entire 'studio-as-instrument' concept which you first start seeing with the likes of Brian Eno et al. Once the gear starts to get hooked to each other, the lines between where one device stops and another starts get very blurry.

Best way of conceiving of generative systems is the 'orders of control' concept which I'd first encountered in academia. Take a single LFO and patch it to a VCO to use it as a modulation source. That's 'one order'. Then take a second LFO, modulate the first LFO with it, and you get two. But the fun starts at 'two orders', because these can either be linear (like the above example) or they can involve feedback paths, such as sending part of the VCO's signal back to the LFO and making use of it to FM the LFO, which then affects how the VCO behaves, which then etc etc etc. Get on up into third orders and beyond, and this can get really involved and interesting.

Another way to break out of straight-up sequencing is to make use of generative variables in your DAW. Ableton Live, these days, is rife with possibilities invoving algorithmic, random, psuedorandom, arithmetical and even more mojoistic methods of generative structuring. Couple some of this with, say, Silent Way and an ES-8 interface in the modular, and then you can even bring these things directly into play in the synth itself...or since the ES-8 has four return lines, just take that 'feedback loop' concept above to utterly insane heights!

DivKid did a video on the Batumi. It has four LFOs in it. You might want to get the Poti expander (also shown in the video).