Hi Bag, and welcome to ATP/NGA!
Can you say more about what you're trying to do, or what you want to find out?
If you ask a question that could be misinterpreted, some wordy bozo like me is likely to come along and yammer on and on about what he's interested in. I'll apologize in advance.
A good place to start with "plant spacing" is whatever the seed packet says. It will probably assume that you grow in long rows, rows only one plant wide, so-so-soil, rather compacted, with a lot of space between rows. Like a farm.
A lot of home gardeners plant differently. They call it many things, like "French Intensive" or "Square Foot Gardening". The short form is: very fertile soil, very loose and well-aerated soil, often in a raised bed, never walked on, so you can cram plants so close together that they shade out the weeds.
You also get more plants per square foot, which MIGHT increase your yields, up to a point, if you have high enough fertility.
To grow that way, first improve your soil with lots of compost! Assure good drainage, enough fertilizer or compost for high fertility, and enough water. Then, instead of "every 8 inches apart, and rows 24" apart", just plant them in 8 inches apart in both directions. Or, if you don't trust the seed packet, 10 inches apart, to be safe.
As with everything in gardening, "your mileage may vary".
If your beds are not very fertile yet, plant farther apart.
If you love to eat them young and tender, sow more seeds much closer together and eat every OTHER plant while they're still small. Really: plant that "8" variety" at 4 inch spacing, but eat half of them before they shade each other too much. (That works better for leafy greens than beans or peas or broccoli!)
If you like to let every plant get up to its maximum size before you harvest it, plant farther apart.
If you grow from seed and have lots of seed, sow closer together.
If you BUY seedlings or "starts", and are not really really rich, plant farther apart.
Thus (as with everything in gardening), the BEST answer is: trial and error. And "it depends".
For your FIRST year growing something, pick some number off a seed packet for spacing, or make it up yourself. Remember, or make notes, on whether that seemed too close or too far apart.
For the SECOND YEAR (or second crop, if you do a Fall crop AND a Spring crop), try a different spacing based on your experience in your yard with your variety of plant. All that matters is what works best FOR YOU.
Really: by the second or third year, you'll realize that MOST garden advice SHOULD begin: "the way it works for ME is ...". And they should all end: "But that's only what works for me."
I think the smart thing is to realize from the beginning that every garden is different, and that this hobby involves experimenting, whether we call it that or not.
For example: growth rate?
For me, at first, that would be exactly 0.0 since I killed all the seeds in several trays. Then, somehow, a few years later, the soil and rain and planting dates must have been "just right". A crop came busting up out of the ground, "like to knocked me on my butt". Most years, somewhere in-between.
I think that professional, scientific gardeners (horticulturalists?) usually refer to a species' or varieties' "maximum growth rate", meaning how fast it grows under totally perfect conditions for rapid growth. (Which might or might not make the best vegetables, or most pest-resistant plants, or highest yield, or most climate-adapted!
I mean, if you put the plant into a sterile growth chamber with roots perfectly inoculated with blah blah MR blah, zero pests, perfect watering, 18 hours of spectrum-perfect lights, fans, extra CO2, and soothing music playing, it will grow much faster than anyone can achieve in an outdoor setting.
