These said pinholes change from each boiling session.
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On the level of molecules, evaporation (and boiling) is when individual molecules escape the loose structure of the liquid and find room to bounce around without being attached to any adjacent neighbor. Liquids have molecules that are pretty well always attached to a few adjacent neighbors, but the molecules are shaking and moving enough that they change attachments a lot (never really keep the same buddies for more than an instant or few). Solids are the same idea, where molecules attach to adjacent neighbors, BUT the molecules lack enough energy to switch partners easily, so once attached to a neighbor, it stays that way for a very long lime.
Boiling is just where there is so much energy in the system that the molecules are bashing into each other a huge amount, and little spots of open space get created. The molecules in that space are so energetic they deny nearby liquid from grabbing them back but happily accept more high-energy gaseous friends (more to push back against the liquid trying to make the bubble go away), so the bubbles grow.
This is normally a relatively random thing, which molecules break free out of all the molecules that are present, so if the entire water body is at the same temperature (more or less the case with rapid boil, convection is transferring the heat throughout, pretty fast), then little bubbles will be forming randomly throughout.
Once a small space in the liquid is forced open, it creates a space for other energetic molecules to escape to. The bubble of gas grows. It also rises because density is lower in the gas phase. So, bubbles just tend to grow upward in size from the base, because bubbles formed at the base will rise and grow while rising and will be bigger than bubbles formed at the midlevel depth (also pressure decreases as bubbles rise so they grow even if they add nothing new, but this is mostly not important over a few inches or several centimeters). There are other bubbles forming nearer surface but they don’t grow as big because they have less time as bubbles. They ALL rise toward the surface though.
That is the general reason why bubbling seems to come from bottom to top. The fact that the base is usually very hot compared to the water is another cause: hotter at the contact surface so more gas gets made right in that immediate zone (has more energy). The hottest spot in the pot is at the base of the water where it sits on the pot.
The question really is why some spots on the bottom seem to be where gas bubbles keep getting made, again and again; when one leaves, a new one starts forming in the very same spot. The reason is mostly that there is a very slight imperfection, a point or edge, and the gas molecules are more likely to grab onto that slightly lower energy position, and thus make a place, again and again, for other molecules to escape to. Such slightly lower energy locations serve as “nucleation points”, meaning that these spots are a lot more likely to see the chemical change happen, because chemical change (and even physical state change like freezing or boiling) are very much a matter of differences in energy, are driven by a “desire” to get to the lowest possible energy state for the conditions, and anything that helps even a little bit will make events a lot more common.
Small imperfections on an otherwise smooth surface become way more likely to see the change happen right there. Small changes in odds show up, to us, as places where the thing is happening a lot more frequently, or regularly. And this keeps happening because the imperfections are not moving around. The imperfections are in and on the surface. Scratches or small points of metal or ceramic, or whatever. Residual solids (baked on solids, perhaps) are also imperfections that favor those spots for any changes that will happen.
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