Sierpinski pentagon
Produce a graphical or ASCII-art representation of a Sierpinski pentagon (aka a Pentaflake) of order 5. Your code should also be able to correctly generate representations of lower orders: 1 to 4.
- See also
Java
<lang java>import java.awt.*; import java.awt.event.ActionEvent; import java.awt.geom.Path2D; import static java.lang.Math.*; import java.util.Random; import javax.swing.*;
public class SierpinskiPentagon extends JPanel {
// exterior angle final double degrees072 = toRadians(72);
/* After scaling we'll have 2 sides plus a gap occupying the length
of a side before scaling. The gap is the base of an isosceles triangle
with a base angle of 72 degrees. */
final double scaleFactor = 1 / (2 + cos(degrees072) * 2);
final int margin = 20; int limit = 0; Random r = new Random();
public SierpinskiPentagon() {
setPreferredSize(new Dimension(640, 640));
setBackground(Color.white);
new Timer(3000, (ActionEvent e) -> {
limit++;
if (limit >= 5)
limit = 0;
repaint();
}).start();
}
void drawPentagon(Graphics2D g, double x, double y, double side, int depth) {
double angle = 3 * degrees072; // starting angle
if (depth == 0) {
Path2D p = new Path2D.Double();
p.moveTo(x, y);
// draw from the top
for (int i = 0; i < 5; i++) {
x = x + cos(angle) * side;
y = y - sin(angle) * side;
p.lineTo(x, y);
angle += degrees072;
}
g.setColor(RandomHue.next());
g.fill(p);
} else {
side *= scaleFactor;
/* Starting at the top of the highest pentagon, calculate
the top vertices of the other pentagons by taking the
length of the scaled side plus the length of the gap. */
double distance = side + side * cos(degrees072) * 2;
/* The top positions form a virtual pentagon of their own,
so simply move from one to the other by changing direction. */
for (int i = 0; i < 5; i++) {
x = x + cos(angle) * distance;
y = y - sin(angle) * distance;
drawPentagon(g, x, y, side, depth - 1);
angle += degrees072;
}
}
}
@Override
public void paintComponent(Graphics gg) {
super.paintComponent(gg);
Graphics2D g = (Graphics2D) gg;
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
int w = getWidth();
double radius = w / 2 - 2 * margin;
double side = radius * sin(PI / 5) * 2;
drawPentagon(g, w / 2, 3 * margin, side, limit); }
public static void main(String[] args) {
SwingUtilities.invokeLater(() -> {
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setTitle("Sierpinski Pentagon");
f.setResizable(true);
f.add(new SierpinskiPentagon(), BorderLayout.CENTER);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
});
}
}
class RandomHue {
/* Try to avoid random color values clumping together */ final static double goldenRatioConjugate = (sqrt(5) - 1) / 2; private static double hue = Math.random();
static Color next() {
hue = (hue + goldenRatioConjugate) % 1;
return Color.getHSBColor((float) hue, 1, 1);
}
}</lang>
Perl 6
Generate an SVG file to STDOUT. Redirect to a file to capture and display it. <lang perl6>constant $order = 5; constant $dim = 1000; constant $sides = 5; constant factor = ( 3 - 5**.5 ) / 2; my @orders = (.6 * $dim) «*» factor «**» (^$order);
my @tr = (0, (-900,1700), (-100,1450), (350,1250), (550,1200), (1000,1000));
INIT say qq:to/STOP/;
<?xml version="1.0" standalone="no"?> <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"> <svg height="{$dim*2}" width="{$dim*2}" version="1.1" xmlns="http://www.w3.org/2000/svg"> STOP
END say '</svg>';
my @vertices = map { cis( $_ * 2 * pi / $sides ) }, ^$sides;
for 0 .. $sides ** $order -> $i {
my $vector = [+] @vertices[$i.base($sides).fmt("%05d").comb] «*» @orders;
say pgon ((@orders[*-1] * (1-factor)) «*» @vertices «+» $vector)».reals».fmt("%0.3f");
};
sub pgon (*@q) {
qq:to/STOP/;
<polygon points="{@q}"
style="fill:blue;stroke:blue;stroke-width:0"
transform="translate({@tr[$order]}) rotate(-18)" />
STOP
}</lang>
Racket
<lang racket>#lang racket/base (require racket/draw pict racket/math racket/class)
- exterior angle
(define 72-degrees (degrees->radians 72))
- After scaling we'll have 2 sides plus a gap occupying the length
- of a side before scaling. The gap is the base of an isosceles triangle
- with a base angle of 72 degrees.
(define scale-factor (/ (+ 2 (* (cos 72-degrees) 2))))
- Starting at the top of the highest pentagon, calculate
- the top vertices of the other pentagons by taking the
- length of the scaled side plus the length of the gap.
(define dist-factor (+ 1 (* (cos 72-degrees) 2)))
- don't use scale, since it scales brushes too (making lines all tiny)
(define (draw-pentagon x y side depth dc)
(let recur ((x x) (y y) (side side) (depth depth))
(cond
[(zero? depth)
(define p (new dc-path%))
(send p move-to x y)
(for/fold ((x x) (y y) (α (* 3 72-degrees))) ((i 5))
(send p line-to x y)
(values (+ x (* side (cos α)))
(- y (* side (sin α)))
(+ α 72-degrees)))
(send p close)
(send dc draw-path p)]
[else
(define side/ (* side scale-factor))
(define dist (* side/ dist-factor))
;; The top positions form a virtual pentagon of their own,
;; so simply move from one to the other by changing direction.
(for/fold ((x x) (y y) (α (* 3 72-degrees))) ((i 5))
(recur x y side/ (sub1 depth))
(values (+ x (* dist (cos α)))
(- y (* dist (sin α)))
(+ α 72-degrees)))])))
(define (dc-draw-pentagon depth w h #:margin (margin 4))
(dc (lambda (dc dx dy)
(define old-brush (send dc get-brush))
(send dc set-brush (make-brush #:style 'transparent))
(draw-pentagon (/ w 2)
(* 3 margin)
(* (- (/ w 2) (* 2 margin))
(sin (/ pi 5)) 2)
depth
dc)
(send dc set-brush old-brush))
w h))
(dc-draw-pentagon 1 120 120) (dc-draw-pentagon 2 120 120) (dc-draw-pentagon 3 120 120) (dc-draw-pentagon 4 120 120) (dc-draw-pentagon 5 640 640)</lang>