7

I'm almost happy with my golden spiral in golden rectangles:

\documentclass[12pt, border=0.5mm]{standalone}

\usepackage{etex}
\usepackage{graphicx}
\usepackage[ngerman]{babel}
\usepackage{pgfplots}
\usepackage{tikz}
\usetikzlibrary{calc, arrows, shapes}
\usepackage{fp}
\usetikzlibrary{fixedpointarithmetic}

\begin{document}

\begin{tikzpicture}[x=1mm, y=1mm]

    \pgfmathsetmacro{\w}{98}        
    \pgfmathsetmacro{\h}{\w*(2/(1+sqrt(5)))}    

    \pgfmathsetmacro{\dx}{(-(\h/(\h-\w))*\w)/((\h/\w) - (\h/(\h-\w)))}      
    \pgfmathsetmacro{\dy}{(\h/\w)*\dx}

    \draw[line width=0.01mm] (0, 0) rectangle (\w, \h);     

    \draw[line width=0.01mm] (\h, 0) -- (\h, \h);       
    \draw[line width=0.01mm] (\h, {\w-\h}) -- (\w, {\w-\h});        
    \draw[line width=0.01mm] ({2*\w-2*\h)}, {\w-\h}) -- ({2*\w-2*\h}, \h);      
    \draw[line width=0.01mm] (\h, {4*\h-2*\w}) -- ({2*\w-2*\h)}, {4*\h-2*\w});
    \draw[line width=0.01mm] ({6*\h-3*\w}, {4*\h-2*\w}) -- ({6*\h-3*\w}, {\w-\h});
    \draw[line width=0.01mm] ({6*\h-3*\w}, {6*\w-9*\h}) -- ({2*\w-2*\h}, {6*\w-9*\h});
    \draw[line width=0.01mm] ({2*\w-2*\h-13*\h+8*\w}, {4*\h-2*\w}) -- ({2*\w-2*\h-13*\h+8*\w}, {4*\h-2*\w-13*\h+8*\w});

    \pgfmathsetmacro{\a}{(-2/pi)*ln((1+sqrt(5))/2)}
    \pgfmathsetmacro{\d}{sqrt(pow(\dx, 2) + pow((\dy - \h), 2))}    

    \draw[rotate around={{-atan((2*\h-\w)/\w)}:(\dx,\dy)}, line width=0.01mm, domain=0:6*pi, variable=\t, samples=5000]
        plot[fixed point arithmetic] ({\dx-\d*exp(\a*\t)*cos(deg(\t))}, {\dy-\d*exp(\a*\t)*sin(deg(\t))});          

\end{tikzpicture}

\end{document}

enter image description here

But even with 5000 samples and very thin lines there is a small problem:

enter image description here

The logarithmic spiral should stay inside the box, but it doesn't. The spirals here have the same problem as mine. Is there a way to fix this?

The line width is not the problem. It's getting even worse with thinner lines of same width:

enter image description here

  • 3
    Is that from the double line width (0.2mm spiral, 0.1mm grid)? Does it vanish if you set the spiral to 0.1mm? – Tom Bombadil Nov 27 '15 at 1:20
  • 1
    Please post complete code! Completing your code in the most obvious way, I just get gazillions of errors. – cfr Nov 27 '15 at 3:03
  • No, the line width is not the problem. – GeMir Nov 27 '15 at 5:45
  • 3
    I believe this is the correct result: The golden spiral passes through the points that divide the golden rectangles, but it's not tangent to the rectangle borders at these points. Take a look at Fig. 34 in Spirals and the Golden Section or see Golden Rectangle on Wolfram MathWorld – Jake Nov 27 '15 at 9:41
  • @Jake An answer? (Or is this off-topic as it's about maths, or ...? – Joseph Wright Dec 17 '15 at 11:12

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