Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]
Groups > comp.programming > #3041
| From | "Chris M. Thomasson" <no@spam.invalid> |
|---|---|
| Newsgroups | comp.programming |
| Subject | Re: A Question About Fractals |
| Date | 2013-02-18 15:53 -0800 |
| Organization | Aioe.org NNTP Server |
| Message-ID | <kfuetu$msp$1@speranza.aioe.org> (permalink) |
| References | <b3b13a29-514f-43b1-9ca7-03ae8189d635@gu9g2000vbb.googlegroups.com> |
"Brian" wrote in message
news:b3b13a29-514f-43b1-9ca7-03ae8189d635@gu9g2000vbb.googlegroups.com...
> Hi, I was reading an article about fractals, and the article says that
> fractals by themselves have no shape or form, but that computers can
> be used to convert fractals into images. What exactly is a fractal?
Self-similarity across various levels of scaling. Think of repeating
patterns that can curve around and repeat themselves at a slightly lower
scale until it hits critical limit. Critical limit can be how far you are
willing to go wrt the infinitely repeating pattern. For instance, a simple
fractal could be something as simple as finding the points of intersections
between a set of cirlces. Then simply draw smaller circles around said
points. Repeat!
FWIW, and since this is comp.programming, here is a retarded first attempt
at creating such circle intersection fractal, presented in AS3 of course!
__________________________________________________________________________
package
{
import flash.display.Sprite;
import flash.events.Event;
/**
* ...
* @author Chris M. Thomasson
*/
public class Main extends Sprite
{
private var mcr1:Number = 3;
private var mcr2:Number = 3;
public function
prv_draw(i:uint, cmp1:Array, cmp2:Array):void {
if (i > 33 || ! cmp1 || ! cmp2) return;
//cmp1[2] * 314628
//.5 / (i / 22)
// c=(i + 1) * (cmp1[2] * cmp1[2]) * (cmp1[2] * cmp1[2]) *
314628
this.graphics.lineStyle(.277 / (i / 22),
0xFFFF00, .03);
prv_circle_draw(cmp1, 0);
if (cmp1 != cmp2)
{
//this.graphics.lineStyle(.75 / (i / 22), 0x00FFFF, 1);
//prv_circle_draw(cmp2, 0);
}
var isect1:Array = prv_circle_isect(cmp1, cmp2, 0, 3);
if (isect1)
{
// prv_circle_draw(isect1, 0);
prv_draw(i + 1, isect1, cmp1);
prv_draw(i + 1, isect1, cmp2);
prv_draw(i + 1, cmp1, isect1);
prv_draw(i + 1, cmp2, isect1);
}
/*
var isect1:Array = prv_circle_isect(cmp1, cmp2, 0, 3);
var isect2:Array = prv_circle_isect(cmp2, cmp1, 0, 3);
if (isect1)
{
prv_circle_draw(isect1, 0);
prv_draw(i + 1, cmp1, isect1);
prv_draw(i + 1, cmp2, isect1);
prv_draw(i + 1, isect1, cmp1);
prv_draw(i + 1, isect1, cmp2);
}
if (isect2)
{
prv_circle_draw(isect2, 0);
prv_draw(i + 1, cmp1, isect2);
prv_draw(i + 1, cmp2, isect2);
prv_draw(i + 1, isect2, cmp1);
prv_draw(i + 1, isect2, cmp2);
}
*/
}
public function
Main():void {
//prv_cdraw_render();
addEventListener(Event.ENTER_FRAME, prv_cdraw_render);
/*
var circles:Array = [
200, 300, 100,
250, 300, 100];
this.graphics.lineStyle(1, 0xFFFFFF);
//prv_circle_draw(circles, 0);
//prv_circle_draw(circles, 3);
//var isect:Array = prv_circle_isect(circles, circles, 0, 3);
//if (! isect) return;
var i:uint = 0;
for (var ci:uint = 0; ci < circles.length && i < 22; ci += 3,
++i)
{
var ci2:uint = ci + 3;
if (ci2 + 3 > circles.length) break;
var isect_fresh:Array =
prv_circle_isect(circles, circles, ci, ci2);
if (! isect_fresh) continue; //fixup?
prv_circle_draw(circles, ci);
prv_circle_draw(isect_fresh, 0);
circles = circles.concat(isect_fresh);
}
*/
/*
prv_circle_draw(isect, 0);
var isect2a:Array = prv_circle_isect(circles, isect, 0, 0);
var isect2b:Array = prv_circle_isect(isect, circles, 0, 3);
prv_circle_draw(isect2a, 0);
prv_circle_draw(isect2b, 0);
var isect3a:Array = prv_circle_isect(circles, isect2a, 0, 0);
var isect3b:Array = prv_circle_isect(isect2b, circles, 0, 3);
prv_circle_draw(isect3a, 0);
prv_circle_draw(isect3b, 0);
//isect2:Array = prv_circle_isect(circles, isect, 0, 0);
*/
}
public function
prv_cdraw_render(e5:Event = null):void {
this.graphics.clear();
var circles:Array = [
355, 300, 222,
555, 300, 177];
this.graphics.lineStyle(1, 0xFFFFFF, .1);
this.graphics.drawCircle(circles[0], circles[1], circles[2]);
this.graphics.drawCircle(circles[3], circles[4], circles[5]);
prv_draw(0, circles, circles);
//var circles2:Array = [
// 200, 100, 333 - mcr2,
// 444, 100, 333 - mcr2];
//this.graphics.drawCircle(circles2[0], circles2[1],
circles2[2]);
//this.graphics.drawCircle(circles2[3], circles2[4],
circles2[5]);
//
// prv_draw(0, circles2, circles);
mcr1 -= .007;
mcr2 += .17;
}
public function
prv_draw_mid_point_circle(
circles:Array,
offset:uint
):Array {
this.graphics.moveTo(circles[0], circles[1]);
var dis:Number = prv_distance(circles, 0);
this.graphics.lineStyle(circles[2]);
this.graphics.lineTo(circles[3], circles[4]);
this.graphics.moveTo(circles[0], circles[1]);
this.graphics.lineStyle(circles[5], 0xFFFF00);
var ggg:Array = prv_mid_point(circles, 0);
this.graphics.lineTo(ggg[0], ggg[1]);
this.graphics.lineStyle(circles[5] + circles[2], 0x3366AA);
this.graphics.drawCircle(ggg[0], ggg[1], dis / 2);
return ggg;
}
public function
prv_distance(
points:Array,
offset:uint
):Number {
var x_diff_sq:Number =
(points[offset + 3] - points[offset]) *
(points[offset + 3] - points[offset]);
var y_diff_sq:Number =
(points[offset + 4] - points[offset + 1]) *
(points[offset + 4] - points[offset + 1]);
return Math.sqrt(x_diff_sq + y_diff_sq);
}
public function
prv_mid_point(
points:Array,
offset:uint
):Array {
var x_mid_pt:Number =
(points[offset] + points[offset + 3]) / 2;
var y_mid_pt:Number =
(points[offset + 1] + points[offset + 4]) / 2;
return [x_mid_pt, y_mid_pt, 0];
}
public function
prv_circle_draw(
circles:Array,
oi:uint
):void {
if (! circles) return;
//this.graphics.beginFill(0xFF0000, .025);
this.graphics.moveTo(circles[oi + 3], circles[oi + 4]);
if (circles[oi + 2] < 33)
{
this.graphics.lineTo(circles[oi + 0], circles[oi + 1]);
/*
this.graphics.drawCircle(
circles[oi + 0],
circles[oi + 1],
circles[oi + 2]);
*/
}
// this.graphics.endFill();
//this.graphics.beginFill(0x0000FF, .025);
this.graphics.moveTo(circles[oi + 0], circles[oi + 1]);
if (circles[oi + 5] < 33)
{
this.graphics.lineTo(circles[oi + 3], circles[oi + 4]);
/*
this.graphics.drawCircle(
circles[oi + 3],
circles[oi + 4],
circles[oi + 5]);
*/
}
//this.graphics.endFill();
}
public function
prv_circle_isect(
circles:Array,
circles2:Array,
ci1:uint,
ci2:uint
):Array {
if (circles[ci1 + 0] == circles2[ci2 + 0] &&
circles2[ci2 + 1] == circles2[ci2 + 1])
{
return null;
}
if (circles[ci1 + 2] < 1 || circles2[ci2 + 2] < 1)
{
return null;
}
var distance:Number =
prv_distance(
circles,
0);
var dx:Number = circles2[ci2 + 0] - circles[ci1 + 0];
var dy:Number = circles2[ci2 + 1] - circles[ci1 + 1];
var d:Number = Math.sqrt((dy * dy) + (dx * dx));
if (d > circles[ci1 + 2] + circles2[ci2 + 2])
{
return null;
}
if (d < Math.abs(circles[ci1 + 2] - circles2[ci2 + 2]))
{
return null;
}
var a:Number =
((circles[ci1 + 2] * circles[ci1 + 2]) -
(circles2[ci2 + 2] * circles2[ci2 + 2]) +
(d * d)) / (2 * d);
var x2:Number = circles[ci1 + 0] + (dx * a / d);
var y2:Number = circles[ci1 + 1] + (dy * a / d);
var h:Number = Math.sqrt((circles[ci1 + 2] * circles[ci1 + 2]) -
(a * a));
// center circle
// this.graphics.drawEllipse(x2 - (h * 2), y2 - h, d * 2, h * 2);
// this.graphics.drawCircle(x2, y2, h);
var rx:Number = -dy * (h / d);
var ry:Number = dx * (h / d);
var p1x:Number = x2 + -h * (circles2[ci2 + 1] - circles[ci1 +
1]) / d;
var p1y:Number = y2 + h * (circles2[ci2 + 0] - circles[ci1 + 0])
/ d;
var p2x:Number = p1x - ((p1x - x2) * 2);
var p2y:Number = p1y - ((p1y - y2) * 2);
/*
this.graphics.drawCircle(p1x, p1x, 10);
this.graphics.drawCircle(p2x, p2y, 10);
this.graphics.moveTo(p1x, p1y);
this.graphics.lineTo(p2x, p2y);
*/
var hr:Number = h / mcr1;
return [p1x, p1y, hr, p2x, p2y, hr];
}
public function
prv_circle_isectx1111(
circles:Array,
ci1:uint,
ci2:uint
):Array {
if (circles[ci1 + 2] < .5 || circles[ci2 + 2] < .5)
{
return null;
}
var distance:Number =
prv_distance(
circles,
0);
var dx:Number = circles[ci2 + 0] - circles[ci1 + 0];
var dy:Number = circles[ci2 + 1] - circles[ci1 + 1];
var d:Number = Math.sqrt((dy * dy) + (dx * dx));
if (d > circles[ci1 + 2] + circles[ci2 + 2])
{
return null;
}
if (d < Math.abs(circles[ci1 + 2] - circles[ci2 + 2]))
{
return null;
}
var a:Number =
((circles[ci1 + 2] * circles[ci1 + 2]) -
(circles[ci2 + 2] * circles[ci2 + 2]) +
(d * d)) / (2 * d);
var x2:Number = circles[ci1 + 0] + (dx * a / d);
var y2:Number = circles[ci1 + 1] + (dy * a / d);
var h:Number = Math.sqrt((circles[ci1 + 2] * circles[ci1 + 2]) -
(a * a));
// center circle
// this.graphics.drawEllipse(x2 - (h * 2), y2 - h, d * 2, h * 2);
// this.graphics.drawCircle(x2, y2, h);
var rx:Number = -dy * (h / d);
var ry:Number = dx * (h / d);
var p1x:Number = x2 + -h * (circles[ci2 + 1] - circles[ci1 + 1])
/ d;
var p1y:Number = y2 + h * (circles[ci2 + 0] - circles[ci1 + 0])
/ d;
var p2x:Number = p1x - ((p1x - x2) * 2);
var p2y:Number = p1y - ((p1y - y2) * 2);
/*
this.graphics.drawCircle(p1x, p1x, 10);
this.graphics.drawCircle(p2x, p2y, 10);
this.graphics.moveTo(p1x, p1y);
this.graphics.lineTo(p2x, p2y);
*/
return [p1x, p1y, h, p2x, p2y, h];
}
public function
prv_circle_isectxx(
circles:Array,
ci1:uint,
ci2:uint
):Array {
if (circles[ci1 + 2] < .5 || circles[ci2 + 3] < .5)
{
return null;
}
var distance:Number =
prv_distance(
circles,
0);
var dx:Number = circles[ci2 + 0] - circles[ci1 + 0];
var dy:Number = circles[ci2 + 2] - circles[ci1 + 1];
var d:Number = Math.sqrt((dy * dy) + (dx * dx));
if (d > circles[ci1 + 2] + circles[ci2 + 3])
{
return null;
}
if (d < Math.abs(circles[ci1 + 2] - circles[ci1 + 3]))
{
return null;
}
var a:Number =
((circles[ci1 + 2] * circles[ci1 + 2]) -
(circles[ci2 + 3] * circles[ci2 + 3]) +
(d * d)) / (2 * d);
var x2:Number = circles[ci1 + 0] + (dx * a / d);
var y2:Number = circles[ci1 + 1] + (dy * a / d);
var h:Number = Math.sqrt((circles[ci1 + 2] * circles[ci1 + 2]) -
(a * a));
// center circle
// this.graphics.drawEllipse(x2 - (h * 2), y2 - h, d * 2, h * 2);
// this.graphics.drawCircle(x2, y2, h);
var rx:Number = -dy * (h / d);
var ry:Number = dx * (h / d);
var p1x:Number = x2 + -h * (circles[ci2 + 2] - circles[ci1 + 1])
/ d;
var p1y:Number = y2 + h * (circles[ci2 + 0] - circles[ci1 + 0])
/ d;
var p2x:Number = p1x - ((p1x - x2) * 2);
var p2y:Number = p1y - ((p1y - y2) * 2);
/*
this.graphics.drawCircle(p1x, p1x, 10);
this.graphics.drawCircle(p2x, p2y, 10);
this.graphics.moveTo(p1x, p1y);
this.graphics.lineTo(p2x, p2y);
*/
return [p1x, p1y, h, p2x, p2y, h];
}
public function
prv_circle_isectx(
circles:Array
):Array {
if (circles[2] < .5 || circles[5] < .5)
{
return null;
}
var distance:Number =
prv_distance(
circles,
0);
var dx:Number = circles[3] - circles[0];
var dy:Number = circles[4] - circles[1];
var d:Number = Math.sqrt((dy * dy) + (dx * dx));
if (d > circles[2] + circles[5])
{
return null;
}
if (d < Math.abs(circles[2] - circles[5]))
{
return null;
}
var a:Number =
((circles[2] * circles[2]) -
(circles[5] * circles[5]) +
(d * d)) / (2 * d);
var x2:Number = circles[0] + (dx * a / d);
var y2:Number = circles[1] + (dy * a / d);
var h:Number = Math.sqrt((circles[2] * circles[2]) - (a * a));
// center circle
// this.graphics.drawEllipse(x2 - (h * 2), y2 - h, d * 2, h * 2);
// this.graphics.drawCircle(x2, y2, h);
var rx:Number = -dy * (h / d);
var ry:Number = dx * (h / d);
var p1x:Number = x2 + -h * (circles[4] - circles[1]) / d;
var p1y:Number = y2 + h * (circles[3] - circles[0]) / d;
var p2x:Number = p1x - ((p1x - x2) * 2);
var p2y:Number = p1y - ((p1y - y2) * 2);
/*
this.graphics.drawCircle(p1x, p1x, 10);
this.graphics.drawCircle(p2x, p2y, 10);
this.graphics.moveTo(p1x, p1y);
this.graphics.lineTo(p2x, p2y);
*/
return [p1x, p1y, h / 1.14, p2x, p2y, h / 1.14];
}
}
}
__________________________________________________________________________
Perhaps it might be of service to your query.
Back to comp.programming | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread
A Question About Fractals Brian <briansipler@yahoo.com> - 2013-01-19 12:10 -0800
Re: A Question About Fractals Geoff <geoff@invalid.invalid> - 2013-01-19 12:45 -0800
Re: A Question About Fractals Brian <briansipler@yahoo.com> - 2013-01-19 13:09 -0800
Re: A Question About Fractals Geoff <geoff@invalid.invalid> - 2013-01-19 14:16 -0800
Re: A Question About Fractals Robin Vowels <robin.vowels@gmail.com> - 2013-01-19 15:53 -0800
Re: A Question About Fractals "Chris M. Thomasson" <no@spam.invalid> - 2013-02-18 15:53 -0800
Re: A Question About Fractals "Chris M. Thomasson" <no@spam.invalid> - 2013-02-18 16:36 -0800
Re: A Question About Fractals "Chris M. Thomasson" <no@spam.invalid> - 2013-02-20 18:25 -0800
Re: A Question About Fractals "Chris M. Thomasson" <no@spam.invalid> - 2013-02-26 02:21 -0800
Re: A Question About Fractals "Chris M. Thomasson" <no@spam.invalid> - 2013-03-03 17:59 -0800
Re: A Question About Fractals luser droog <mijoryx@yahoo.com> - 2013-05-17 18:55 -0700
Re: A Question About Fractals "Chris M. Thomasson" <no@spam.invalid> - 2013-05-17 22:27 -0700
Re: A Question About Fractals "Chris M. Thomasson" <no@spam.invalid> - 2013-03-04 13:17 -0800
Re: A Question About Fractals "Chris M. Thomasson" <no@spam.invalid> - 2013-03-10 18:10 -0700
Re: A Question About Fractals "Chris M. Thomasson" <no@spam.invalid> - 2013-03-10 18:21 -0700
Re: A Question About Fractals James Dow Allen <gmail@jamesdowallen.nospam> - 2013-02-19 17:45 +0000
Re: A Question About Fractals "Chris M. Thomasson" <no@spam.invalid> - 2013-02-19 13:11 -0800
csiph-web