Oh boy, the hours I spent creating ferns on my Atari ST 520 with affine transformations....
Amazingly, now that I think about it, sparked by an article in the British newspaper the Guardian. Which ran a computing page every Thursday. Do newspapers still carry such intelligent content?
Also amazingly that numberphile link led me to a vid about mathematicians trying to solve a problem about moving a sofa around a corner. I recall Douglas Adams describes a computer stuck in and endless loop trying to figure out how to move a sofa up some stairs and around a corridor....
The CAD software I use has a module that does this. It's a lot of fun to build pathological cases and watch it solve.
It employs some methods first. Then randomized those. Then it will employ a binary tree of sorts exploring movement combinations.
When all else fails, it will just thrash randomly.
Solution times get exponential quick. The thing does get there by brute force eventually, though I've seen it take days.
That feature is used by the auto industry to evaluate whether it's possible to service complex things once assembled. It has the most trouble with "barely fits through" scenarios, often getting close, then random thrashing, until some exit possibility is found.
If you want, it can be watched real time. Slower that way, but a lot of fun.
Comments
I make that about three and a half thousand instructions per test.
Seems a bit low, but maybe I have miscalculated. Or perhaps most of the tests take less work than than I expect.
Added 20170403:
Coloring Collatz Conjecture (extra footage) - Numberphile
Collatz and Self Similarity
https://en.wikipedia.org/wiki/Barnsley_fern
-Phil
Amazingly, now that I think about it, sparked by an article in the British newspaper the Guardian. Which ran a computing page every Thursday. Do newspapers still carry such intelligent content?
Also amazingly that numberphile link led me to a vid about mathematicians trying to solve a problem about moving a sofa around a corner. I recall Douglas Adams describes a computer stuck in and endless loop trying to figure out how to move a sofa up some stairs and around a corridor....
It employs some methods first. Then randomized those. Then it will employ a binary tree of sorts exploring movement combinations.
When all else fails, it will just thrash randomly.
Solution times get exponential quick. The thing does get there by brute force eventually, though I've seen it take days.
That feature is used by the auto industry to evaluate whether it's possible to service complex things once assembled. It has the most trouble with "barely fits through" scenarios, often getting close, then random thrashing, until some exit possibility is found.
If you want, it can be watched real time. Slower that way, but a lot of fun.
-Phil
Jim