Matlab: compute Moore curve help.

Question

Lam Chun Ting 2012-5-18

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/38785-matlab-compute-moore-curve-help

回答： Henning U. Voss 2023-8-1

Compute the fractal curve based on the following L  system
Moore curve, 4 steps
Axiom: XFX+F+XFX
Production rules:
Newx=-YF+XFX+FYNewy=+
XF-YFY-FX+
Constants: α= π/2; θ=π/2

The following is my answer for Moore curve.But I know it's not a right curve, Because the picture is not same as what I have seen on wikipedia. I really don't know where am I go wrong. May anyone help me to slove this please? Many thanks for helping!!!

function [X,Y]=Moore_curve(Lmax)
  Axiom='XFX+F+XFX';
  Newf='F';
  Newx='-YF+XFX+FY';
  Newy='+XF-YFY-FX+';
  theta=pi/2;
  alpha=pi/2;  
  p=[0;0];
  p=Coord(p,Lmax,Axiom,Newf,Newx,Newy,alpha,theta);
  M=size(p,2); 
  X=p(1:1,1:M); 
  Y=p(2:2,1:M); 
  figure(1); 
  plot(X,Y,'Color','k'); 
  set(gca,'xtick',[],'ytick',[]);
  set(gca,'XColor','w','YColor','w');
  function z=Coord(p,Lmax,Axiom,Newf,Newx,Newy,alpha,theta)
  Rule=Moore_syst(Lmax,Axiom,Newf,Newx,Newy,1,'');
  M=length(Rule);
  for i=1:M
  Tmp=p(1:2,size(p,2):size(p,2));
  if Rule(i)=='F'
  R=[cos(alpha);sin(alpha)];
  R=R/(2^Lmax);
  Tmp=Tmp+R;
  p=cat(2,p,Tmp);
  end
  if Rule(i)=='+'
  alpha=alpha+theta;
  end
  if Rule(i)=='-'
  alpha=alpha-theta;
  end;
  end
  z=p;
  function z1=Moore_syst(Lmax,Axiom,Newf,Newx,Newy,n,tmp)
  if n<=Lmax
  if n==1
  tmp=Axiom;
  end
  M=length(tmp);
  tmp1='';
  for i=1:M
      if tmp(i)=='F'
          tmp1=strcat(tmp1,Newf);
      end
  if tmp(i)=='X'
  tmp1=strcat(tmp1,Newx);
  end
  if tmp(i)=='Y'
  tmp1=strcat(tmp1,Newy);
  end
  if not(tmp(i)=='F') &&not(tmp(i)=='X') &&not(tmp(i)=='Y')
  tmp1=strcat(tmp1,tmp(i));
  end
  end
  tmp=tmp1;
  n=n+1;
  tmp=Moore_syst(Lmax,Axiom,Newf,Newx,Newy,n,tmp);
  end
  z1=tmp;