I have always wanted to create an ultra realistic Von Neumann probe simulation... I explained what I wanted to ChatGPT....

It understood, and so after a couple of hours of back and forth I now have a mathematical point cloud representation of the galaxy... I wanted it to be extremely realistic, so the milky way has been broken up into many millions of little 'cells' The density of stars in these cells is determined by data based Astronomy models of the Milky way- density of stars is highest in the core, of course and also simulates the barred spiral galaxy in star distribution. Not only that, I plan to add a representation of the how the population density of ages and classes of star vary as you go from the core to the rim based on astronomical models of our galaxy- so the user can, for instance, exclude entire classes of stars from the Von Neuman colonization- (my bet is that it makes almost no difference to the time to colonize the galaxy if you choose to colonize ALL stars or JUST G2V sun class stars) - for instance the user can decide that binary star systems (~50% of systems) should be excluded because there is little hope of finding life there, or decide they are only interested in sun-like stars. Totally pointless detail because, I am almost certain it will make nearly zero difference to the time it takes for the probes to populate the subset of stars chosen for exploration.

I even included an Astrophysical model for the dust distribution in the galaxy, because the 'death rate' of probes may increase or the speed may need to decrease- or both- where dust density is higher... again, pointless detail.... 420 lines of code to generate a pointlessly detailed galaxy so far... and almost at the point where I can add and model the growth of a von Neumann population..

This is, of course, a problem that has already been solved... the answer really depends on the speed the probes can reach... if one Intelligence successfully creates such a machine and sets it loose, then its 10's-100's of millions of years to populate the galaxy with that time primarily set by the top speed you assume for the probe...

Why am I doing it? No good reason... As a kid I was fascinated by the Fermi Paradox and the idea that if one intelligence built such a machine 100's of millions of years ago or more, then we should have one in our solar system... so where are they? And of course there is the Fred Saberhagen 'Berserker' stories that propose malevolent Von Neumann machines systematically killing off competing intelligences as a solution to the Fermi paradox...

I also find it amusing to use AI to help model it, because- after it exterminates the annoying humans- it very well might go on to populate the galaxy - so maybe the simulation will give it a head start... :) With just 2.25 million 'cells' it takes my computer less than a second to create my galaxy... 50 million points takes 10 seconds and it still renders smoothly, but once I add all the data to turn each point into a cell containing 10,000 stars I will have o render a small subset and essentially only calculate for the the colonization 'wavefront' as it expands... ultimately I want to take the model of the expansion and export it into Blender to make a 3d animation that the camera can fly around and into....