POV-Ray : Newsgroups : povray.advanced-users : Pappus Chain : Re: Pappus Chain Server Time
18 Jul 2024 07:34:39 EDT (-0400)
  Re: Pappus Chain  
From: Bald Eagle
Date: 19 Jun 2024 09:55:00
Message: <web.6672e21b3bd24dfede5e631125979125@news.povray.org>
"Bald Eagle" <cre### [at] netscapenet> wrote:
> Just posting this here for reference.
>
> https://www.johndcook.com/blog/2023/12/19/conformal-map-disk-triangle/
>
> Would be cool to apply this to the gasket to see what pops out - probably a
> Sierpinski Triangle.
>
> Search: conformal mapping of circle to a triangle
>
> - BE

https://www.mathworks.com/matlabcentral/fileexchange/35008-generation-of-random-variates

https://www.mathworks.com/matlabcentral/fileexchange/1844-gaussian-hypergeometric-function

function z=hypergeometric2f1(a,b,c,x,n)
% HYPERGEOMETRIC2F1 Computes the hypergeometric function
% using a series expansion:
%
%    f(a,b;c;x)=
%
%    1 + [ab/1!c]x + [a(a+1)b(b+1)/2!c(c+1)]x^2 +
%    [a(a+1)(a+2)b(b+1)(b+2)/3!c(c+1)(c+2)]x^3 + ...
%
% The series is expanded to n terms
%
% This function solves the Gaussian Hypergeometric Differential Equation:
%
%     x(1-x)y'' + {c-(a+b+1)x}y' - aby = 0
%
% The Hypergeometric function converges only for:
% |x| < 1
% c != 0, -1, -2, -3, ...
%
%
% Comments to:
% Diego Garcia   - d.g### [at] ieeeorg
% Chuck Mongiovi - mon### [at] fastnet
% June 14, 2002
if nargin ~= 5
    error('Usage: hypergeometric2f1(a,b,c,x,n) --> Wrong number of arguments')
end
if (n <= 0 | n ~= floor(n))
    error('Usage: hypergeometric2f1(a,b,c,x,n) --> n has to be a positive
integer')
end
if (abs(x) > 1)
    error('Usage: hypergeometric2f1(a,b,c,x,n) --> |x| has to be less than 1')
end
if (c <= 0 & c == floor(c))
    error('Usage: hypergeometric2f1(a,b,c,x,n) --> c != 0, -1, -2, -3, ...')
end
z = 0;
m = 0;
while (m<n)
    if (m == 0)
        delta = 1;
    else
        delta = delta .* x .* (a + (m - 1)) .* (b + (m-1)) ./ m ./ (c + (m-1));
   end
   z = z + delta;
   m = m + 1;
end


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