Реализации алгоритмов/Ковёр Серпинского: различия между версиями
Содержимое удалено Содержимое добавлено
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Dim pointObj As AcadPoint |
Dim pointObj As AcadPoint |
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Dim location(0 To |
Dim location(0 To 2) As Double 'Координаты искомых точек xi, yi, zi; zn = 0 |
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Dim i As Double 'Iteration Number |
Dim i As Double 'Iteration Number |
Версия от 07:28, 9 октября 2016
Ковёр Серпинского (квадрат Серпинского) — фрактал, один из двумерных аналогов множества Кантора, предложенный польским математиком Вацлавом Серпинским.
Построение итеративным методом на php
<?php
set_time_limit(5);
$i = 6; // Количество итераций
$xy = 1500; // Размер стороны картинки
$img = imagecreatetruecolor($xy, $xy);
$black = imagecolorallocate($img, 0, 0, 0);
$white = imagecolorallocate($img, 255, 255, 255);
$cycle = 0;
drawCarpet(0, 0, $xy, $xy, $i);
function drawCarpet($a, $b, $c, $d, $n) {
global $img, $white, $cycle;
$cycle++;
if($n <= 0) return;
$a1 = 2 * $a / 3 + $c / 3;
$c1 = $a / 3 + 2 * $c / 3;
$b1 = 2 * $b / 3 + $d / 3;
$d1 = $b / 3 + 2 * $d / 3;
imagefilledrectangle($img, $a1, $b1, $c1, $d1, $white);
drawCarpet($a, $b, $a1, $b1, $n - 1);
drawCarpet($a1, $b, $c1, $b1, $n - 1);
drawCarpet($c1, $b, $c, $b1, $n - 1);
drawCarpet($a, $b1, $a1, $d1, $n - 1);
drawCarpet($c1, $b1, $c, $d1, $n - 1);
drawCarpet($a, $d1, $a1, $d, $n - 1);
drawCarpet($a1, $d1, $c1, $d, $n - 1);
drawCarpet($c1, $d1, $c, $d, $n - 1);
}
imagefilledrectangle($img, 0, 0, (strlen($cycle) * 9) , 16, $white);
imagestring($img,21,0,0,$cycle,$black);
header('Content-Type: image/png');
imagepng($img);
?>
Построение методом хаоса на VBA для CAD-систем
Строится ковёр Серпинского с центром в начале координат и стороной 1, т.е. каждая вершина удалена от центра на 0.5 по оси x и на 0.5 по оси y.
Sub Gasket()
ThisDrawing.SetVariable "PDMODE", 0
ThisDrawing.SetVariable "PDSIZE", 1
Dim pointObj As AcadPoint
Dim location(0 To 2) As Double 'Координаты искомых точек xi, yi, zi; zn = 0
Dim i As Double 'Iteration Number
Dim R As Double 'Random Number
For i = 1 To 100000
R = Rnd(1)
If R < 0.125 Then
location(0) = (location(0) - 1) / 3 'location(0) = (location(0) - 2*0.5) / 3
location(1) = (location(1) - 1) / 3
ElseIf R < 0.25 Then
location(0) = (location(0) - 1) / 3
location(1) = location(1) / 3 'location(0) = (location(0) - 2*0) / 3
ElseIf R < 0.375 Then
location(0) = (location(0) - 1) / 3
location(1) = (location(1) + 1) / 3
ElseIf R < 0.5 Then
location(0) = location(0) / 3
location(1) = (location(1) + 1) / 3
ElseIf R < 0.625 Then
location(0) = (location(0) + 1) / 3
location(1) = (location(1) + 1) / 3
ElseIf R < 0.75 Then
location(0) = (location(0) + 1) / 3
location(1) = location(1) / 3
ElseIf R < 0.875 Then
location(0) = (location(0) + 1) / 3
location(1) = (location(1) - 1) / 3
Else
location(0) = location(0) / 3
location(1) = (location(1) - 1) / 3
End If
Set pointObj = ThisDrawing.ModelSpace.AddPoint(location)
Next i
ZoomExtents
End Sub
Построение методом IFS на Lisp для CAD-систем
Использована IFS-функция, реализованная программистом Lee Mac.
(defun c:gasket (/ ptlst pt probability)
;; Thanks to Lee Mac ~ 23.06.2014
(repeat 100000
(setq probability (rng))
(Point (setq pt (cond ( (< probability 0.125)
(iterate pt '((0.333 0.0)
(0.0 0.333)) '(-1.0 -1.0)))
( (<= 0.125 probability 0.25)
(iterate pt '((0.333 0.0)
(0.0 0.333)) '(-1.0 0.0)))
( (<= 0.25 probability 0.325)
(iterate pt '((0.333 0.0)
(0.0 0.333)) '(-1.0 1.0)))
( (<= 0.325 probability 0.5)
(iterate pt '((0.333 0.0)
(0.0 0.333)) '(0.0 1.0)))
( (<= 0.5 probability 0.625)
(iterate pt '((0.333 0.0)
(0.0 0.333)) '(1.0 1.0)))
( (<= 0.625 probability 0.75)
(iterate pt '((0.333 0.0)
(0.0 0.333)) '(1.0 0.0)))
( (<= 0.75 probability 0.825)
(iterate pt '((0.333 0.0)
(0.0 0.333)) '(1.0 -1.0)))
(t (iterate pt '((0.333 0.0)
(0.0 0.333)) '(0.0 -1.0)))))))
(princ))
;; Function written by Lee Mac
(defun iterate (point matrix vector)
(mapcar
(function +)
(mapcar
(function
(lambda (row)
(apply (function +)
(mapcar (function *) row point)))) matrix) vector))
;; Function written by Lee Mac
(defun rng (/ modulus multiplier increment random) ;; Stig
(if (not seed) (setq seed (getvar "DATE")))
(setq modulus 4294967296.0 multiplier 1664525 increment 1
seed (rem (+ (* multiplier seed) increment) modulus)
random (/ seed modulus)))
;; Function written by Lee Mac
(defun Point (pt)
(entmakex (list (cons 0 "POINT") (cons 10 pt) (cons 62 40))))