Time for an 2014 update…
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Ingy döt Net
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2520 changed files with 34227 additions and 7318 deletions
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package {
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import flash.display.Sprite;
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import flash.events.Event;
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public class VanDerCorput extends Sprite {
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public function VanDerCorput():void {
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if (stage) init();
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else addEventListener(Event.ADDED_TO_STAGE, init);
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}
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private function init(e:Event = null):void {
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removeEventListener(Event.ADDED_TO_STAGE, init);
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var base2:Vector.<Number> = new Vector.<Number>(10, true);
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var base3:Vector.<Number> = new Vector.<Number>(10, true);
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var base4:Vector.<Number> = new Vector.<Number>(10, true);
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var base5:Vector.<Number> = new Vector.<Number>(10, true);
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var base6:Vector.<Number> = new Vector.<Number>(10, true);
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var base7:Vector.<Number> = new Vector.<Number>(10, true);
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var base8:Vector.<Number> = new Vector.<Number>(10, true);
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var i:uint;
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for ( i = 0; i < 10; i++ ) {
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base2[i] = Math.round( _getTerm(i, 2) * 1000000 ) / 1000000;
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base3[i] = Math.round( _getTerm(i, 3) * 1000000 ) / 1000000;
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base4[i] = Math.round( _getTerm(i, 4) * 1000000 ) / 1000000;
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base5[i] = Math.round( _getTerm(i, 5) * 1000000 ) / 1000000;
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base6[i] = Math.round( _getTerm(i, 6) * 1000000 ) / 1000000;
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base7[i] = Math.round( _getTerm(i, 7) * 1000000 ) / 1000000;
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base8[i] = Math.round( _getTerm(i, 8) * 1000000 ) / 1000000;
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}
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trace("Base 2: " + base2.join(', '));
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trace("Base 3: " + base3.join(', '));
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trace("Base 4: " + base4.join(', '));
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trace("Base 5: " + base5.join(', '));
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trace("Base 6: " + base6.join(', '));
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trace("Base 7: " + base7.join(', '));
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trace("Base 8: " + base8.join(', '));
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}
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private function _getTerm(n:uint, base:uint = 2):Number {
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var r:Number = 0, p:uint, digit:uint;
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var baseLog:Number = Math.log(base);
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while ( n > 0 ) {
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p = Math.pow( base, uint(Math.log(n) / baseLog) );
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digit = n / p;
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n %= p;
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r += digit / (p * base);
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}
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return r;
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}
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}
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}
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@ -0,0 +1,25 @@
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(defn van-der-corput
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"Get the nth element of the van der Corput sequence."
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([n]
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;; Default base = 2
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(van-der-corput n 2))
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([n base]
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(let [s (/ 1 base)] ;; A multiplicand to shift to the right of the decimal.
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;; We essentially want to reverse the digits of n and put them after the
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;; decimal point. So, we repeatedly pull off the lowest digit of n, scale
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;; it to the right of the decimal point, and accumulate that.
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(loop [sum 0
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n n
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scale s]
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(if (zero? n)
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sum ;; Base case: no digits left, so we're done.
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(recur (+ sum (* (rem n base) scale)) ;; Accumulate the least digit
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(quot n base) ;; Drop a digit of n
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(* scale s))))))) ;; Move farther past the decimal
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(clojure.pprint/print-table
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(cons :base (range 10)) ;; column headings
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(for [base (range 2 6)] ;; rows
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(into {:base base}
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(for [n (range 10)] ;; table entries
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[n (van-der-corput n base)]))))
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@ -0,0 +1,6 @@
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| :base | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
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|-------+---+-----+-----+-----+------+------+------+-------+-------+-------|
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| 2 | 0 | 1/2 | 1/4 | 3/4 | 1/8 | 5/8 | 3/8 | 7/8 | 1/16 | 9/16 |
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| 3 | 0 | 1/3 | 2/3 | 1/9 | 4/9 | 7/9 | 2/9 | 5/9 | 8/9 | 1/27 |
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| 4 | 0 | 1/4 | 1/2 | 3/4 | 1/16 | 5/16 | 9/16 | 13/16 | 1/8 | 3/8 |
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| 5 | 0 | 1/5 | 2/5 | 3/5 | 4/5 | 1/25 | 6/25 | 11/25 | 16/25 | 21/25 |
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@ -0,0 +1,11 @@
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/* convert a decimal integer to a list of digits in base `base' */
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dec2digits(d, base):= block([digits: []],
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while (d>0) do block([newdi: mod(d, base)],
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digits: cons(newdi, digits),
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d: round( (d - newdi) / base)),
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digits)$
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dec2digits(123, 10);
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/* [1, 2, 3] */
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dec2digits( 8, 2);
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/* [1, 0, 0, 0] */
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@ -0,0 +1,9 @@
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/* convert a list of digits in base `base' to a decimal integer */
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digits2dec(l, base):= block([s: 0, po: 1],
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for di in reverse(l) do (s: di*po + s, po: po*base),
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s)$
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digits2dec([1, 2, 3], 10);
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/* 123 */
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digits2dec([1, 0, 0, 0], 2);
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/* 8 */
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@ -0,0 +1,19 @@
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vdc(n, base):= makelist(
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digits2dec(
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dec2digits(k, base),
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1/base) / base,
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k, n);
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vdc(10, 2);
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/*
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1 1 3 1 5 3 7 1 9 5
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(%o123) [-, -, -, -, -, -, -, --, --, --]
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2 4 4 8 8 8 8 16 16 16
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*/
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vdc(10, 5);
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/*
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1 2 3 4 1 6 11 16 21 2
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(%o124) [-, -, -, -, --, --, --, --, --, --]
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5 5 5 5 25 25 25 25 25 25
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*/
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@ -0,0 +1,21 @@
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/* 11 in decimal is */
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digits: digits2dec([box(1), box(0), box(1), box(1)], box(2));
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aux: expand(digits2dec(digits, 1/base) / base)$
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simp: false$
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/* reflected this would become ... */
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subst(box(2), base, aux);
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simp: true$
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/*
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3 2
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""" """ """ """ """ """ """
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(%o126) "2" "1" + "2" "0" + "2" "1" + "1"
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""" """ """ """ """ """ """
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- 4 - 3 - 2 - 1
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""" """ """ """ """ """ """ """
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(%o129) "1" "2" + "0" "2" + "1" "2" + "1" "2"
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""" """ """ """ """ """ """ """
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*/
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