04 NOV 2018 by ideonexus

 A Computer Algorithm for Randomization

Back in the early days of computers, one of the more popular methods of generating a sequence of random numbers was to employ the following scheme: 1. Choose a starting number between 0 and 1. 2. Multiply the starting number by 4 ("stretch" it). Subtract 4 times the square of the starting number from the quantity obtained in step 2 ("fold" the interval back on itself in order to keep the final result in the same range). 3.Given a starting number between 0 and 1, we can use the proce-dure...
Folksonomies: algorithms randomization
Folksonomies: algorithms randomization
  1  notes

From John Casti.

29 JAN 2014 by ideonexus

 1/9998 Produces Binary Output

The pattern will break down once you get past 8192, which is 2^13. That means that the pattern continues for an impressive 52 significant figures (well, it actually breaks down on the 52nd digit, which will be a 3 instead of a 2). The reason it works is that 9998 = 10^4 - 2. You can expand as   1 / (10^n - 2) = 1/10^n * 1/(1 - 2/10^n) = 1/10^n * (1 2/10^n 2^2 /10^2n 2^3 /10^3n ...) which gives the observed pattern. It breaks down when 2^k has more than n digi...
Folksonomies: games math puzzles
Folksonomies: games math puzzles
  1  notes
 
29 MAY 2013 by ideonexus

 Simple Explanation of Big O Notation

The simplest definition I can give for Big-O notation is this: Big-O notation is a relative representation of the complexity of an algorithm. There are some important and deliberately chosen words in that sentence: relative: you can only compare apples to apples. You can't compare an algorithm to do arithmetic multiplication to an algorithm that sorts a list of integers. But two algorithms that do arithmetic operations (one multiplication, one addition) will tell you something meaningful; re...
 1  1  notes

One of the best, down-to-Earth explanations of a concept that can get incredibly complex.

26 MAR 2013 by ideonexus

 π in Base-26 Will Produce All the Works of Shakespeare

Base 26 is one of two fairly natural ways of representing numbers as text using a 26-letter alphabet. The number of interest is expressed numerically in base 26, and then the 26 different base-26 digits are identified with letters as 0=A, 1=B, 2=C, ... 25=Z. Here are the first 100 digits of pi expressed in this way: D.DRSQLOLYRTRODNLHNQTGKUDQGTUIRXNEQBCKBSZIVQQVGDMELM UEXROIQIYALVUZVEBMIJPQQXLKPLRNCFWJPBYMGGOHJMMQISMS... Lo! At the 6th digit we find a two-letter word (LO), and only a ...
 2  2  notes

By assigning letters to numbers in the irrational number, we can produce the effect of a million monkeys on a million typewriters for a million years.

12 JUN 2012 by ideonexus

 The Magical Number Seven

What about the magical number seven? What about the seven wonders of the world, the seven seas, the seven deadly sins, the seven daughters of Atlas in the Pleiades, the seven ages of man, the seven levels of hell, the seven primary colors, the seven notes of the musical scale, and the seven days of the week? What about the seven-point rating scale, the seven categories for absolute judgment, the seven objects in the span of attention, and the seven digits in the span of immediate memory? For ...
  1  notes

Occurs in many cultural artifacts, but there is not obvious profundity to the number.