My developmental psych prof made a declaration I have found to be largely if not completely true:
There are 2 types of babies/children; Lump Babies & Adventurers.
Lump Babies are the (often sunny disposition, but not always) children who wait to have the world come to them. The stay where you put them to greater or lesser degree, they play with what you give them, they wait to be approached by others completely confident that others will approach them. These are the kids that do "independent play" from a young age, and parents can use things like playpens, babygates, coloring books, blocks, a specific drawer that is "theirs" etc., to keep them occupied. She estimates that about 2/3s to 3/4s of babies fall into the 'lump' category. And in all her experience (40 years of working with children clinically & in research & her own children) is of the opinion that Lumps are born... NOT "created" by parents, although most parents claim the credit for them. (She says she, too, claimed credit for her first 2 children... until she had her third and realized NOPE! Personality is not created by parenting).
Adventurers do NOT wait for the world to come to them... but seek it out, often at full speed. They climb, crawl, run, and generally attack the world. Parents CANNOT leave them to "play independently" but instead need to keep eyes on them at all times to prevent disaster... or just get used to disaster. If a child who is an adventurer is *afraid* of climbing (happens), they instead develop TREMENDOUS lungs... absolutely demanding to be let out/ picked up/ and are generally inconsolable. These are the children who will scream for HOURS if confined in some place they are afraid to climb from, but are immediately happy the moment they are "let loose on the world".
((The names, btw, are intentionally "backwards". Both are accurately descriptive, but any sane parent wants the 'lump' which sounds awful, and while 'adventure' sounds sexy and all... it's really an exercise in preventing accidental suicide in the child's case and intentional in the parents' case... because it's several years of NEVER having a break unless you have someone else take care of them from time to time.))
Like I said, I've found her statement to be amazingly true. (Both in my own child and in several dozen other children I've cared for, and several hundred I've observed.).
It's soooooo not parenting... just personality.
Personally, not only having an 'adventure baby', but also who turned out to be an ADHD kiddo (he could run 3 miles by the age of 2 without stopping, take a 10 minute break, and be going again at full speed for another couple hours)... I got him hooked on video games at the age of 2, and got him into 'outside classes' at about the same time (like gymnastics).
The video games were AMAZING. Oh. My. God. An actual HOUR of peace while I knew his bum was safely glued to a chair. I made the mistake of having them be educational video games (www.starfall.com) which meant he was reading fluently by 3 (creating a whole other depth of 'accidental suicide watch'... toddlers take warning labels like directions, they really have no impulse control at that age... nor discrimination; Enquirer has as much value to them as the NYT). But we all make out mistakes. Outside classes were phenom, because YEP! someone else had him for an hour of huge grinned running excitement.
My son needed CONSTANT supervision until about age 5. I can't even count the number of "things" I did to feed that insatiable curiosity of his. But that's what it came down to. If I wanted him to stay halfway safe... he needed THINGS to explore. And a lot of them. The computer was my favorite tool, but anything complex could keep him absorbed for at least a little while before he was the streak of lightening determined to make it to Madagascar by lunchtime or bust.