# The Lumber Room

"Consign them to dust and damp by way of preserving them"

## How does Tupper’s self-referential formula work?

[I write this post with a certain degree of embarrassment, because in the end it turns out (1) to be more simple than I anticipated, and (2) already done before, as I could have found if I had internet access when I did this. :-)]

The so-called “Tupper’s self-referential formula” is the following, due to Jeff Tupper.

Graph the set of all points ${(x,y)}$ such that

$\displaystyle \frac12 < \left\lfloor \mathrm{mod} \left( \left\lfloor{\frac{y}{17}}\right\rfloor 2^{-17\lfloor x \rfloor - \mathrm{mod}(\lfloor y \rfloor, 17)}, 2 \right) \right\rfloor$

in the region

$\displaystyle 0 < x < 106$

$\displaystyle N < y < N+17$

where N is the following 544-digit integer:
48584506361897134235820959624942020445814005879832445494830930850619
34704708809928450644769865524364849997247024915119110411605739177407
85691975432657185544205721044573588368182982375413963433822519945219
16512843483329051311931999535024137587652392648746133949068701305622
95813219481113685339535565290850023875092856892694555974281546386510
73004910672305893358605254409666435126534936364395712556569593681518
43348576052669401612512669514215505395545191537854575257565907405401
57929001765967965480064427829131488548259914721248506352686630476300

The result is the following graph:

Figure 1: The graph of the formula, in some obscure region, is a picture of the formula itself.

Whoa. How does this work?

At first sight this is rather too incredible for words.

But after a few moments we can begin to guess what is going on, and see that—while clever—this is perhaps not so extraordinary after all. So let us calmly try to reverse-engineer this feat.

Written by S

Tue, 2011-04-12 at 13:05:20

Posted in mathematics

Tagged with , , ,

## WordPress theme that defies description

and my understanding:

Now someone explain how this works :)

Written by S

Fri, 2008-03-28 at 05:45:24

Posted in Uncategorized

Tagged with , ,

For those who haven’t seen a demonstration of cold reading before, here is an excellent one:

Thanks to “A Candle in the Dark”, a blog that turned up in my Google recommended feeds.

Written by S

Mon, 2008-02-18 at 21:52:48

Posted in Uncategorized

Tagged with ,

## Film I saw

The LSC plays movies every weekend, to which I get free admission, and I usually watch all the films, no matter how bad I expect them to be :-)

Yesterday I saw 1408. It is a horror film based on a Stephen King short story. (It is about room 1408 of the Dolphin Hotel, where…)

The movie isn’t bad at all. It even has a happy ending. (The director’s cut apparently doesn’t.)

I saw a poster that said it

ranks with The Shining as one of the best Stephen King adaptations ever.

Obviously, the guy forgot about The Shawshank Redemption.

One might argue that Shawshank wasn’t a horror movie, but then again, neither was The Shining.
Really: Watch the trailer, it’s hilarious:
[Created by Robert Ryang. A contest-winning entry.]
Read the rest of this entry »

Written by S

Mon, 2007-10-22 at 04:30:59