Puzzle Description:

This image is the third iteration of the procedure that leads to the Sierpinski carpet. The construction of the Sierpinski carpet begins with a square. The square is cut into 9 congruent subsquares in a 3-by-3 grid, and the central subsquare is removed. The same procedure is then applied recursively to the remaining 8 subsquares, ad infinitum. (To get a better feel for these iterations, visit http://www.shodor.org/interactivate/activities/SierpinskiCarpet ). Now the INTERESTING part!!!! If the original square is 1 foot by 1 foot, then after the first iteration, the area is 8/9 square feet. At each step, you are removing 1/9 of the remaining area. So after two iterations, the area is (8/9)^2 (i.e., eight-ninths times itself). Here, in the picture shown, the area is then (8/9)^3 = (8/9) x(8/9)x(8/9). But if we let the number of iterations go to infinity, we are multiplying 8/9 times itself over and over again. The result of doing that is that the area eventually becomes ZERO!

#1: Petra Lassen (stjarna) on Feb 19, 2009 [SPOILER]

Fun puzzle, complicated maths!

Amazing!!!!!!!

Cool. Just like Sierpinski's Triangle!

Reminds me of fractals. Here is a flash actionscript that is only 4k and really pretty:
http://www.zenbullets.com/automatons/Tree.swf

And since we are all into pixels, here is a pixel flash that is less than 1k. (I'll bet Jan knows how to make cool stuff like this.)
http://krazydad.com/bestiary/bestiary_random_pixels.html

Thanks for your entry!

If you like things like this, take a look at this Mandelbrot Fractal video:
http://www.youtube.com/watch?v=WAJE35wX1nQ

Here's a webpbn puzzle (naturgirl's first one) that looks like a Sierpinski Triangle:
http://webpbn.com/index.cgi?id=2025

Nice links, Teresa! That Mandelbrot movie reminds me that as you zoom in on the full-blown Sierpinski carpet, it looks exactly the same as the zoomed-out view.

Watching all the movies inspired me to do a pattern. At least it is in B/W so it won't make anyone go cross eyed.

http://webpbn.com/index.cgi?id=5094

Would you believe I was thinking Sierpinski as soon as I read the title?

Excellent!!

I hadn't heard of this pattern, so I just thought it looked cool, so it was nice to discover it's cool /and/ interesting :D

Math math, blah blah blah... LOL

Echoing Adam.

Comment Suppressed:Click below to view hints

I once wrote a program on my TI-81 that generated a Sierpinski triangle. That was fun! This puzzle, as a puzzle, not so fun - but I enjoyed reading about the math. :)

Comment Suppressed:Click below to view hints

I think that infinite processes take forever. Also, the area of the rug only approaches zero, but I don't believe it actually becomes zero.

Show: Hints

Goto next topic

You must register and log in to be able to participate in this discussion.