fantastic and interesting video. Would you share your image file. I would like to print it out in a poster size and it is similar to a real world problem I am solving. Again, nice video and thanks for taking the time to create it.
You are awesome! I really appreciate sincerity with which you are making strangers educated with this stuff, with no direct benefits to you whatsoever!!! Thanks!!!!
this is interesting...btw, the tower of hanoi game featured in this video was the javascript application that i submitted to dynamicdrive website. i have created a new version on facebook, just search for "JavaScript Tower of Hanoi".
thanks for the video, fascinating, couldn't stop grinning when i saw the recursive possibilities taking on a fractal shape. Looking forward to more. :)
1. Coloring out the odd numbers in Pascal's triangle.
2. Draw a tringle and a random point(pt1) into the triangle, randomly pick one of the 3 vertex and draw a dot on the middle of the imgainary line between pt1 and that vertex. Repeat with the middle point being now the new start point.
@7hkey There's many more than that too :) I'm actually thinking of making a video about this alone. All the ways of generating the thing. There's also cellular automata way, bitwise XOR's, etc... like 7 ways or something :D
@TheDarkSagan I guess you could say... Google? Wikipedia? haha. But not even that because I knew most of what I'm teaching you for a very long time from somewhere. I don't think there is any software. Or you can search "Iterated Function System" or something on google for some applets that can generate fractals.
@casualcuber Ading more disks only increases the depth of the Sierprinski triangle fractal. You would get the actual infinitely deep Sierpinski triangle if you had infinite number of disks, and 3 pegs. Any graph can exist in 3 dimensions, no need to ever go to 4th.
Game play of Towers of Hanoi is also recursive. After playing with it for a few minutes, I found a very simple way to get the minimum number of moves for any number of disks. A little hard to explain in words, but I basically see it as moving the whole stack but the bottom to another peg, and you do that by moving the whole stack you're going to move but the bottom to a different peg, and so on. Repeat until solved.
Anyway, great video! I knew I wasn't the only one that finds math interesting.
@bluecobra95 "Game play of Towers of Hanoi is also recursive...."
This is exactly the same algorithm which is used to write a Tower of Hanoi computer program. In most programming languages, you can solve the puzzle using less than 12 lines of program code (although it's more if you incorporate a graphical display). Since most programs are measured in the tens of thousands of lines of code, to get so much function for so little code is quite remarkable.
@TheTurtleman9 Yes, it's interesting to think of what other games have state spaces that are fractal. The crucial point here is that Towers of Hanoi is recursive: It can be broken down to smaller instances of the same problem. To solve Hanoi4: First solve Hanoi3 going to left, move purple disk right, then solve Hanoi3 again moving everything from left to right. Checkers is harder... for example is checkers on board of size 5x5 related somehow to checkers on board of size 4x4? That's the question
Dude, you totally should make more videos!
whiterottenrabbit 1 month ago
1:32 - Who lost?
XanglesPrime 1 month ago
if this game is played on 4 pegs would it make a square fractal?
ophios 5 months ago
I've notice something interesting also:
R-Red
B-Blue
G-Green
P-Pink
This is the sequence in order to solve the problem (both right and left placement.)
RBR G RBR P RBR G RBR
pmfa91 7 months ago
fantastic and interesting video. Would you share your image file. I would like to print it out in a poster size and it is similar to a real world problem I am solving. Again, nice video and thanks for taking the time to create it.
gomanred1 10 months ago
This is so amazing!
Can you share or point to where this ToH drawing (sierpinski visualization) is?
I would be grateful.
paroxyzm21 10 months ago
You are awesome! I really appreciate sincerity with which you are making strangers educated with this stuff, with no direct benefits to you whatsoever!!! Thanks!!!!
lifedeathatoz 1 year ago
this is interesting...btw, the tower of hanoi game featured in this video was the javascript application that i submitted to dynamicdrive website. i have created a new version on facebook, just search for "JavaScript Tower of Hanoi".
noypiscripter 1 year ago
What if you increase the disks? does it break (Become unsolvable)?
What if you increase the pegs again? I want to see more :D
If you increase the pegs to infinity, what happens?
Diehanddieverletzt 1 year ago
Great video! I really like this approach!
You might like my paper fractals videos and also I have a Towers of Hanoi tutorial.
Among other math stuffs.
TyYann 1 year ago
thanks for the video, fascinating, couldn't stop grinning when i saw the recursive possibilities taking on a fractal shape. Looking forward to more. :)
l3xrun 1 year ago
This so cool. I knew these two:
1. Coloring out the odd numbers in Pascal's triangle.
2. Draw a tringle and a random point(pt1) into the triangle, randomly pick one of the 3 vertex and draw a dot on the middle of the imgainary line between pt1 and that vertex. Repeat with the middle point being now the new start point.
7hkey 1 year ago
@7hkey There's many more than that too :) I'm actually thinking of making a video about this alone. All the ways of generating the thing. There's also cellular automata way, bitwise XOR's, etc... like 7 ways or something :D
fractalmath 1 year ago
@fractalmath well, would surely be interesting, and I'm already subscribed ;)
7hkey 1 year ago
Great Video. What software are you using to find the fractals?
TheDarkSagan 1 year ago
@TheDarkSagan I guess you could say... Google? Wikipedia? haha. But not even that because I knew most of what I'm teaching you for a very long time from somewhere. I don't think there is any software. Or you can search "Iterated Function System" or something on google for some applets that can generate fractals.
fractalmath 1 year ago
@fractalmath Okay , so drew the diagram of the towers of Hanoi fractal yourself?
TheDarkSagan 1 year ago
@TheDarkSagan no... I googled Towers of Hanoi graph :s
fractalmath 1 year ago
@fractalmath Cool thanks.
TheDarkSagan 1 year ago
If you added a sixth disk, would the corresponding fractal only be able to exist in the 4th dimension?
casualcuber 1 year ago
@casualcuber Ading more disks only increases the depth of the Sierprinski triangle fractal. You would get the actual infinitely deep Sierpinski triangle if you had infinite number of disks, and 3 pegs. Any graph can exist in 3 dimensions, no need to ever go to 4th.
fractalmath 1 year ago
Game play of Towers of Hanoi is also recursive. After playing with it for a few minutes, I found a very simple way to get the minimum number of moves for any number of disks. A little hard to explain in words, but I basically see it as moving the whole stack but the bottom to another peg, and you do that by moving the whole stack you're going to move but the bottom to a different peg, and so on. Repeat until solved.
Anyway, great video! I knew I wasn't the only one that finds math interesting.
bluecobra95 1 year ago
@bluecobra95 "Game play of Towers of Hanoi is also recursive...."
This is exactly the same algorithm which is used to write a Tower of Hanoi computer program. In most programming languages, you can solve the puzzle using less than 12 lines of program code (although it's more if you incorporate a graphical display). Since most programs are measured in the tens of thousands of lines of code, to get so much function for so little code is quite remarkable.
mandolinic 1 year ago
I wonder if there's a fractal related to a game like checkers.
TheTurtleman9 1 year ago
@TheTurtleman9 Yes, it's interesting to think of what other games have state spaces that are fractal. The crucial point here is that Towers of Hanoi is recursive: It can be broken down to smaller instances of the same problem. To solve Hanoi4: First solve Hanoi3 going to left, move purple disk right, then solve Hanoi3 again moving everything from left to right. Checkers is harder... for example is checkers on board of size 5x5 related somehow to checkers on board of size 4x4? That's the question
fractalmath 1 year ago