Fractals and Towers of Hanoi

Fractals have a habit of popping up all over the place. This video we look at a game called
Towers of Hanoi.

Play Towers of Hanoi:
http://www.dynamicdrive.com/dynamicindex12/towerhanoi.htm

Towers of Hanoi rules, bit more, and the picture:
http://www.jaapsch.net/puzzles/hanoi.htm

4 pegs:
http://www.exocortex.org/toh/TowerOfHanoiGraphs.html

Category:

Pets & Animals

Tags:

• towers
• hanoi
• fractal
• sierpinski
• triangle
• state
• space
• math

[7hkey]

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.

[fractalmath]

@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]

Great Video. What software are you using to find the fractals?

[fractalmath]

@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.

[TheDarkSagan]

@fractalmath Okay , so drew the diagram of the towers of Hanoi fractal yourself?

[fractalmath]

@TheDarkSagan no... I googled Towers of Hanoi graph :s

[whiterottenrabbit]

Dude, you totally should make more videos!

[XanglesPrime]

1:32 - Who lost?

[ophios]

if this game is played on 4 pegs would it make a square fractal?

[pmfa91]

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

[gomanred1]

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.

[paroxyzm21]

This is so amazing!

Can you share or point to where this ToH drawing (sierpinski visualization) is?

I would be grateful.

[lifedeathatoz]

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!!!!

[noypiscripter]

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".

[mandolinic]

@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.

[Diehanddieverletzt]

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?