Hello there.
This is Numberphile. We mainly post videos about mathematics and just numbers in general.
This is Numberphile. We mainly post videos about mathematics and just numbers in general.
This Numberphile video about red and black knights (and more so it’s accompanying Numberphile2 video) resulted in some astounding patterns and images.
I recommend viewing them both for full context before scrolling further.
I have since received many emails from people who have delved further and created their own images and simulators, etc.
It’s impossible to list them all, but I have collated some here. Sorry if I missed you out, this selection is quite random. But I did look at every email…
Most messages have been edited and truncated… and I cannot vouch for any of the links.
Chris B:
I have made a web version of the tool; the source code is still at the github link if you're interested to read it, but if you just want to play around with the visualisation then you can access that here: 3D Knight Tool. It's still a work in progress so you'll have to forgive the occasional bug/glitch. Once you've seen all the pre-defined scenes that I came up with, the most interesting thing to do is to open the "edit leapers & scenes" dialog and change some of the parameters in there - the "leapers" box defines each of the pieces, which are then referenced in the "scenes" box - it should be mostly intuitive but I'm happy to answer any questions you have about how the interface works.
Here is what the ball looks like with two traditional knights of two colours (one blue, one red) at radius 80:
As an aside, I've just added a new piece that I'm calling a "spider", which moves in a (2, 1, 3) pattern - when paired with the wazir's (1, 0, 0), you get this pretty interesting looking ball (the "3D Spiders vs Wazir" scene from the tool):
Alekas R:
Watched your recent numberphile video about different patterns that can arise from chess knights interacting on a spiralling board, and ended up finding a rather pretty pattern myself, so thought I'd share it with you. This one is not from real chess pieces, these being my three pieces possible movements:
And this is the result:
Seems odd from afar, but when zooming in on the left quadrant it's a very quaint repeating mountain range:
