MonkeyWithTheHat

Showing posts with label formula. Show all posts

Math formula that when graphed, produces an image of the formula itself

Tupper's self-referential formula is a self-referential formula defined by Jeff Tupper that, when graphed in two dimensions, can visually reproduce the formula itself. It is used in various math and computer science courses as an exercise in graphing formulae.
The formula was first published in his 2001 SIGGRAPH paper that discusses methods related to the GrafEq formula-graphing program he developed.
The formula is an inequality defined by:

${1\over 2} < \left\lfloor \mathrm{mod}\left(\left\lfloor {y \over 17} \right\rfloor 2^{-17 \lfloor x \rfloor - \mathrm{mod}(\lfloor y\rfloor, 17)},2\right)\right\rfloor$

If one graphs the set of points (x,y-k) with $0 \le x \le 106$ and $k \le y \le k + 17$ such that they satisfy the inequality given above, the resulting graph looks like this:

Tupper's self referential formula plot.png

This formula itself is a general purpose method of decoding a bitmap stored in the constant k, so it could actually be used to draw any other image. When applied to the unbounded positive range $0 \le y$ , the formula tiles a vertical swath of the plane with a pattern that contains all possible 17 pixel tall bitmaps. (from: wikipedia)

56 Comments

Pizza mathematics

pizza, pic, math, formula, how pizza name is made funny

And god said, let there be light, and there was light

The Longest Equation Ever Known to Man

Standard Model Lagrangian (density)

The standard what?

The Standard Model is the current Theory which governs all known strong and electroweak interactions. This includes basically everything that has EVER been measured by humans (sans gravity). It really is the best Theory that we have. It has been fantastically successful in predicting and explaining data; there are no obvious or overt violations of this Theory. Nerds can go read (or add more information :/) about it here.

How long did it take to type?

In it's current form, the actual equation have took about four hours (spread over almost a week) to write into a file using LaTeX. And sadly, the typist think there is a sign error somewhere, but he just don't have the energy to hunt it down.

13 Comments

Batman Graph Mathematical Equation

Batman graph equation


where is batman?

bat man in ms excel

You might also like,

The Love Formula : How to Draw a Heart Shaped Curvy Graph

12 Comments

The Love Formula : How to Draw a Heart Shaped Curvy Graph

Ever wanted to know how to draw a heart shaped graph?
Is that real? well yes.
There are a number of mathematical curves that produced heart shapes, some of which are illustrated below.

The first curve is a rotated cardioid (whose name means "heart-shaped") given by the polar equation

(1)

The second is obtained by taking the

cross section of the heart surface and relabeling the

-coordinates as

, giving the order-6 algebraic equation

(2)

The third curve is given by the parametric equations

			(3)
			(4)

where

(H. Dascanio, pers. comm., June 21, 2003). The fourth curve is given by

(5)

(P. Kuriscak, pers. comm., Feb. 12, 2006). Each half of this heart curve is a portion of an algebraic curve of order 6. And the fifth curve is the polar curve

Source: HeartCurve