Thank you and have a good knight.
Knight Vision

I recently went through a similar exercise. I set a knight in the center of the board and put a black pawn on all the squares it attacked. Then I put a white piece (I ran out of pawns) on the squares that would be attacked by the black pawns if they were knights. It became clear that even though a knight isn't as good as a bishop on open ground it can still cover a large area very quickly if it's centralized.
I think it's a good idea to experiment with pieces this way. The more points of view you have when looking at a board the more possibilities you may see.

d7 and b5 are "missing" in that last diagram.
Interesting way to look at how a peice's power is much greater in the centre.
Ooops! I knew I'd make a mistake somewhere. Thanks for pointing that out.

Interesting topic. When I play I just seem to naturally know where the Knights will go and what threats they pose when there but I have never seen a post as good as this at visually outlining why Knights are (generally) so much better in the centre. This is extra advantageous for teaching people how to use a Knight in an attacking sense as I think the Knight is probably the hardest piece for a beginner to learn.

There is an old chess problem called the "Knight's Tour." Basically, you put the knight on a random square, and make it visit every single square on the board without visiting one twice. Use counters to mark where you've been. It is possible, but extremely difficult.
That may help with your Knight vision.
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This may be really trivial stuff to the more seasoned players here, but I have had a small epiphany and would like to share.
I was thinking about knights and in my studies, I had always been shown the classic pattern of eight squares around the knight depicting the squares it can move to. That's great to know. But it doesn't really help me find a fork. I found myself in a game where there was a combination that I could play that would leave me with two knights vs. a knight and bishop. I became fearful because I really didn't feel comfortable with my knights. Sure I knew how they moved and have forked my fair share of peices, but the knights always seemed very mysterious.
I had the idea that instead of visualizing the squares that the knight can move to, it might be better to visualize the squares that the knight can attack on the next move. I went to the board and mapped it out. The result really surprised me I have never seen the knights portrayed like this.
I didn't know they had so much range.
I now understand why Knights are said to be worse than bishops in open positions (slightly less board coverage) but better in closed positions (its target squares are unblockable).
This pattern it makes it much easier for me to find targets and forks for my knight. I can find the targets first, then search for the square I need to move to.
When I think of sayings like "A knight on the rim is grim" it makes even more sense. If you visualize the knight's attack squares, it really brings the point home.
The knight in the corner is truly pathetic.
I think that mastery of the Knight is one of the most important skills any chess player can learn. In my mind, visualizing the knights like this allows me to search for squares that are two moves ahead without calculation.
Please share any other ideas you have on improving Knight vision.
Best Regards,
Okolo