Apollonian Gasket: Now uses equations
lazarus / 39-Graphics

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Boleeman · 2024-06-08 05:53

An Apollonian Gasket made by using IFS and another that uses
equations.


Made a new one using BgraBmp, quadratic formula and ellipse (3rd reply
below)
A bit sluggish. Need to fill it with colours,


Would love to work out how to make a nested version.

On https://codegolf.stackexchange.com/questions/38450/draw-an-
apollonian-gasket  it can be implemented as a javascript function to
draw an SVG of it. I wonder if this could be converted and used with
BgraBmp to draw that Nested Apollonian Gasket.
http://jsfiddle.net/8L8kwa1p/2/

Here is the Javascript function:
Code: Pascal  [Select][+][-]window.onload = function(){var x1 =
document.getElementById("main_content_section"); if (x1) { var x =
document.getElementsByClassName("geshi");for (var i = 0; i  function
A(s){P='<svg width=800 height=800><g fill=none stroke=red
transform=translate(400,400)>';Q=[];s=eval(s);S=-400*s[0][0];function
d(c){P+='<circle r='+Math.abs(S/c[0])+' cx='+S*c[1]/c[0]+'
cy='+S*c[2]/c[0]+' />'}for(c=4;c--
;d(s[0]),s.push(s.shift()))Q.push(s.slice());for(;s=Q.shift();d(c)){c=
[];for(i=4;i--;)c[i]=2*(s[0][i]+s[1][i]+s[2][i])-
s[3][i];for(i=6;c[0]<S&&i;)Q.push([s[i--%3],s[i--
%3],c,s[i%3]])}document.body.innerHTML=P} A('[[-6, 0, 0], [10, 2/3,
0], [15, -3/2, 0], [19, -5/6, 2]]');


There is also a Hyperbolic version that looks cool.

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AlexTP · 2024-06-08 06:26

Saved to https://github.com/Alexey-T/Boleeman_Curves

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Boleeman · 2024-06-08 09:57

Here is the version that uses equations.

In NEED of a SPEED RENDERING IMPROVEMENT

Not Fill coloured yet, but can be coloured manually in Paint.

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domasz · 2024-06-08 10:09

Is the code up to date? When I try to run I get divide by zero:
Code: Pascal  [Select][+][-]window.onload = function(){var x1 =
document.getElementById("main_content_section"); if (x1) { var x =
document.getElementsByClassName("geshi");for (var i = 0; i
results[0].Value := -b / (2 * a);

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Dzandaa · 2024-06-08 11:04

Hi,
I also have division by Zero at

Code: Pascal  [Select][+][-]window.onload = function(){var x1 =
document.getElementById("main_content_section"); if (x1) { var x =
document.getElementsByClassName("geshi");for (var i = 0; i
results[0].Value := -b / (2 * a);
B->

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Josh · 2024-06-08 13:00

hi

just looked at code in v2.

can you replace and see if it works. added some checks

Code: Pascal  [Select][+][-]window.onload = function(){var x1 =
document.getElementById("main_content_section"); if (x1) { var x =
document.getElementsByClassName("geshi");for (var i = 0; i function
TForm1.QuadraticSolutions(a, b, c: Double): TDoubleValueList;const 
tiny = 0.01;var  discriminant: Double;  results:
TDoubleValueList;begin  // Prevent division by a very small number  if
Abs(a) < tiny then Exit;  SetLength(results, 0);  discriminant := b *
b - 4 * a * c;  if discriminant < 0 then Exit;  if Abs(discriminant) <
tiny then  begin    // 1 root    SetLength(results, 1);   
results[0].Value := -b / (2 * a);    Result := results;    Exit; 
end;  // 2 roots  SetLength(results, 2);  results[0].Value := (-b +
Sqrt(discriminant)) / (2 * a);  results[1].Value := (-b -
Sqrt(discriminant)) / (2 * a);  Result := results;end;

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AlexTP · 2024-06-08 14:57

1. 'results' var is not needed, since you can use Result var.
2. func result is not inited if 1st or 2nd Exit runs!
Add line
  Result:= nil;
at the start.

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Boleeman · 2024-06-09 11:05

Thanks for the fixes. For some reason I did not get divide by zero
error on Win 10 OS.

Might be good to make threaded to speed up the rendering.