having fun with aximate

The "jumping centipede":
    $num = 10;
    $norm = 0;
    $damp = 1.4;
    foreach $i (1..$num) {
	$norm += 1/sqrt($damp**$i);
    }
    $xx = -120;
    $nballs = 16;
    $height = 80;
    foreach (1..$nballs) {
	$bound1 = 0;
	$bound2 = 0;
	$bound3 = 0;
	$height += 40/$nballs;
	$xx += 15;
	$i=0;
	while ($bound2 < 100) {
	    $i++;
	    $bound2 += 100/$norm/sqrt($damp**$i)*sqrt($height/100);
	    $bound3 = $bound1 + 100/$norm/sqrt($damp**$i)/2*sqrt($height/100);
	    point({"coordinates" => [[$xx,-50],[$xx,$height/$damp**($i-1)-50]],
		   "interval" => [$bound1,$bound3]},
		  {"coordinates" => ['$t','(1-$t)**2']});
	    point({"coordinates" => [[$xx,$height/$damp**($i-1)-50],[$xx,-50]],
		   "interval" => [$bound3,$bound2],
		   "staythere" => 0},
		  {"coordinates" => ['$t','$t**2']});
	    $bound1 = $bound2;
	}
    }
An example from physics: elliptically polarized wave:
    $p2 = point({"type" => "empty",
    	 "coordinates" => [[50,50],[-100,-100]]});
	 
    track("c1",{%{$p2},"color" => "Blue"});
    $total = 10;
    foreach $n (0..($total-1)) {
	$interval = [100/$total*$n,100],
	$subtr = 1-1/$total*$n;
	$p1 = point({"type" => "empty",
		     "coordinates" => [[]],
		     "interval" => $interval},
		    {"coordinates" => ['50*cos(3*pi*$t*'.$subtr.
				       ') + 50 - 150*($t*'.$subtr.')',
				       '70*sin(3*pi*($t*'.$subtr.
				       '))+ 50 - 150*($t*'.$subtr.')']});
	
	track("cx".$n,{%{$p1},"color" => "Red"});
	line({"arrow" => 1,
	      "foot" => [[]],
	      "head" => [[]],
	      "interval" => $interval
	     },
	     {"foot" => ['50-150*($t*'.$subtr.')',
			 '50-150*($t*'.$subtr.')'],
	      "head" => ['50*cos(3*pi*($t*'.$subtr.
			 ')) + 50 - 150*($t*'.$subtr.')',
			 '70*sin(3*pi*($t*'.$subtr.
			 '))+ 50 - 150*($t*'.$subtr.')']});
     }
Here we are randomly distributing 1000 points. However, we want to do this only in the first frame of the movie. The rest is done by the evolution. The variable $aximate::IGLOB counts the frames, starting from 0.
    foreach $i (0..1000) {
        if ($aximate::IGLOB==1) {
            $r = 100*sqrt(rand(1));
            $phi = 2*pi*rand(1);
            @xpos1 = (@xpos1,$r*cos($phi));
            @ypos1 = (@ypos1,$r*sin($phi));
            @ampx = (@ampx,50*rand(1));
            @ampy = (@ampy,50*rand(1));
            @phase = (@phase,2*pi*rand(1));
        }
        point({"type" => "ccirc",
               "color" => "Red",
               "bethere" => 0,
               "radius" => [[3]],
               "coordinates" => [[]],
               "polar" => [[]]},
            {"coordinates" => [$xpos1[$i].'+'.$ampx[$i].'*sin(2*pi*$t+'.
                 $phase[$i].')',
                               $ypos1[$i].'+'.$ampy[$i].'*cos(2*pi*$t+'.
                 $phase[$i].')']});
    }

And some more, without source code...

stoss1 – a simple scattering reaction basic elements
ggh1 – a Feynman diagram (gluon fusion) connecting objects; attaching text
wheel1 – a spinning wheel using do-loops; "circular"=1
wurf1 – throwing a ball changing time-evolution
fallingdisk1 – falling disk just for fun
jumpingball2 – jumping ball do-loop; evolve; "loop"=1
federpendel1 – mass on a spring evolve
spiral1 polar coordinates
fadenpendel1 – mass on a string evolve
main