Cellular Automata Method for Generating Random Cave-Like Levels. It is an old and fairly well documented trick to use cellular automata to generate cave-like structures.
The basic idea is to fill the first map randomly, then repeatedly create new maps using the 4-5 rule: a tile becomes a wall if it was a wall and 4 or more of its nine neighbors were walls, or if it was not a wall and 5 or more neighbors were. Put more succinctly, a tile is a wall if the 3x3 region centered on it contained at least 5 walls. Game Theory. MathPuzzle.com. Fractals, The Colors Of Infinity Part 1. Blog Archive » A brief history of problems that ruined my world. Calculus Video Tutorials. Photopic Sky Survey. Tupper's self-referential formula. 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. where denotes the floor function and mod is the modulo operation. Let k equal the following 543-digit integer: If one graphs the set of points (x, y) in and satisfying the inequality given above, the resulting graph looks like this (note that the axes in this plot have been reversed, otherwise the picture comes out upside-down): The 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.
. , the formula tiles a vertical swath of the plane with a pattern that contains all possible 17-pixel-tall bitmaps. Download Graphic Images from the Hillis/Bull Lab. Return to "Download Files" Page You are welcome to download the following graphic image of the Tree of Life for non-commercial, educational purposes: Tree of Life (~3,000 species, based on rRNA sequences) (pdf, 368 KB) (see Science, 2003, 300:1692-1697)
Calculus Mega Cheat Sheet. Nerd Paradise : Divisibility Rules for Arbitrary Divisors. It's rather obvious when a number is divisible by 2 or 5, and some of you probably know how to tell if a number is divisible by 3, but it is possible to figure out the division 'rule' for any number.
Here are the rules for 2 through 11... The last digit is divisible by 2. The sum of all the digits in the number is divisible by 3. The last 2 digits are divisible by 4. The last digit is 5 or 0. 11 cheap gifts guaranteed to impress science geeks. Science comes up with a lot of awesome stuff, and you don't need a Ph.D, a secret lab, or government funding to get your hands on some of the coolest discoveries.
We've got a list of 11 mostly affordable gifts that are guaranteed to blow your mind, whether or not you're a science geek. Click on any image to see it enlarged. 1. PatrickJMT. Blue Solver. World Sunlight Map. Unit Conversions. How Differential Gear works must see 100% Doodling in Math Class: Snakes + Graphs. How to Hunt Elephants. MATHEMATICIANS hunt elephants by going to Africa, throwing out everything that is not an elephant, and catching one of whatever is left.
EXPERIENCED MATHEMATICIANS will attempt to prove the existence of at least one unique elephant before proceeding to step 1 as a subordinate exercise. PROFESSORS OF MATHEMATICS will prove the existence of at least one unique elephant and then leave the detection and capture of an actual elephant as an exercise for their graduate students. COMPUTER SCIENTISTS hunt elephants by exercising Algorithm A: Go to Africa. Technically, the Glass is Always Full. I-Heart-Math_210-l.jpg (JPEG Image, 600x400 pixels) Wolfram. Solve Your Calculus Problems Online. Long Division of Polynomials. Unsolved Problems. What does 0^0 (zero raised to the zeroth power) equal? Why do mathematicians and high school teachers disagree.
Clever student: I know!
Now we just plug in x=0, and we see that zero to the zero is one! Cleverer student: No, you’re wrong! You’re not allowed to divide by zero, which you did in the last step. Weierstrass functions. Weierstrass functions are famous for being continuous everywhere, but differentiable "nowhere".
Here is an example of one: It is not hard to show that this series converges for all x. In fact, it is absolutely convergent. Six ways to write more comprehensible code. I learned to write, clear, maintainable code the hard way.
For the last twelve years, I've made my living writing computer games and selling them over the Net using the marketing technique that was once charmingly known as shareware. What this means is that I start with a blank screen, start coding, and, a few tens of thousands of lines of code later, I have something to sell. This means that, if I make a stinky mess, I'm doing it in my own nest.