The Sierpinski triangle page to end most Sierpinski triangle pages
oftenpaper.net
oftenpaper.net
When I was about 11 (mid 80s) our school got a shining new computer lab with original IBM 8086 PCs, and one teacher improvised a LOGO class. After a while we were divided into two groups of more advanced kids and the rest of the class. I was in the advanced team, and I think I was the only kid there who didn't have a computer at home and hadn't coded before. Anyway, we were learning about recursion, and the teacher gave us increasingly difficult tasks.
Then one day he showed us this triangle thingie, and told us to write an algorithm to draw it for the next class. I was shocked and stuck. Remember, I had no interwebs or even books on the subject. I spent hours in the computer lab banging at it, and couldn't do it. I went home, worried that I'll be the only one in the class who failed to do it - and that I'll be taken out of the advanced group. I was horrified, I was literally crying over it.
Then while taking a shower or something like that, the solution suddenly hit me. I ran to the school lab (it was open after hours) wrote the code and it worked. The joy and adrenaline rush of it was something out of this world, let alone the relief that I wouldn't be "downgraded" from the advanced class.
The next day in class, the teacher asked us to show him our code. It turned out I was the only kid who figured it out. It was one of the proudest moments of my life I guess, and I've been trying to recreate that rush of solving a hard task ever since.
Nice, vive Pascal but then I discovered that Pascal wasn't portable but C was so down to Pascal and here goes C (which I still like despite its numerous flaws)!
I'm going to take them up again soon as I have found a fancy furniture shop that would like to retail them for me.
I've always wanted to make them out of pyrex glass rod however it would be quite difficult at first. I do have some glassblowing chops though.
http://www.warplife.com/mdc/books/schizoaffective-disorder/v...
The photograph is taking looking upwards at one suspended from the ceiling. I would wind them up then let go, gravity lead the string to unwind, quickly at first then quite slow. It's a very pleasant phenomenon.
I may make a very large one for Burning Man this year.
"So I was me and I was in math class watching paint dry it was starting to crack when suddenly I realized there was a page for which the internet was invented. I set out to create that page, ultimately succeeding with the sierpinski triangle page to end most sierpinski triangle pages ™.
...
So while the sierpinski triangle page to end most sierpinski triangle pages ™ purports to be some kind of exploratory rundown of the Sierpinski triangle, it's also a fractal expression of just how carried away I get..."
It's math like I like my music: when the author takes the subject seriously without taking themselves too seriously.
I am amazed every time I come across this page again... such seemingly effortlessly playful exploration of math and geometry...
[Edit] Which makes me realize that the submitter for the original was him: https://news.ycombinator.com/user?id=pr_fancycorn - so that may lead to some way to contact him.
I quickly decided it was a shame to let a perfectly good compiler go to waste and learned C.
Most 640x400 images were taking 25-32 hours to produce, depending on where they were. I started writing a fixed-point library, and then found Fractint and just wrote a graphics driver for the Sperry adapter. The same images generated in only 8 minutes.
Tell that to the kids today, and they won't believe you.
On the site...Pascal's triangle (%2 and other mods) is particularly fascinating to me.
There's a playground for this here: http://stestagg.github.io/Sierp.js/ - chrome/ff only
If you want to play around with this kind of recursive shapes, I would suggest to try out http://GeoKone.NET, it's an application I've developed that let's you create this kind of formations interactively in your browser.
Well, at least the kind of formations on the first half of the page or so.
For example, of course you find the Sierpinski pattern under disjointness. Here's some LiveScript to handle disjointness with integers representing bitwise vectors of "x is in the set" (1) or "x is not in the set" (0):
fmt = (x) -> if x then 'o' else ' '
display = console.log . (.join '\n') . (.map (.join '')) . (.map (.map fmt))
display [[(x .&. y) == 0 for y from 0 to 63] for x from 0 to 63]
(x, y) (x + 2^n, y)
(x, y + 2^n) (x + 2^n, y + 2^n)
Now, of course if you find a Sierpinski triangle under the is_disjoint_from relation, you find it under the is_subset_of operation -- because A is disjoint from B if and only if B is a subset of the set-complement of A. So as long as your picture "mirrors" in one axis under set complements, of course you're going to see the same pattern for subsets as for disjoints.
The same thing happens when the author says, "The binary operation I found in our little binary binomial table was NOTing n, ANDing the result with k, and then NOTing that: ¬(¬n∧k) = n∨¬k." If you have had a logic course, this result "either A or not-B" should look like the expression for "A implies B", a statement that in all the possibilities that we are thinking about, knowing that you are in a situation where A is true means that you know that you're in a situation where B is also true.
Or, put a different way, the situations where B is true are a subset of the situations where A is true. So you can take the subset-of relation and immediately turn it into that binary formula; and conversely this explains why the author complains, "I had to list the subsets in precisely this order to get the right result" -- basically, you have to count in binary to get the right result. (To go the other way you just need the "all true" value -- that is, this formula "A or not B" must hold for all circumstances, so subset-of would in the above code look like `63 == (x .|. 63 - y)`.)
TCL? :P