[Tex/LaTex] Playing around with a Rubik’s Cube in TikZ

randomtikz-pgftikz-styles

My questions are:

Is there a possibility to get a view of a Rubik's Cube in TikZ such as in pgfplots; like view={NUMBER1}{NUMBER2}?
How can be the Rubik's Cube be scrambled with a number a, such that this number makes a random pattern to the cube (→ scrambeling).

Here is my MWE (it's just the Cube without any functions):

\documentclass[border=5pt,tikz]{standalone}
\usetikzlibrary{3d}
\begin{document}
    \begin{tikzpicture}[every node/.style={inner sep=1cm,draw,very thick},very thick]
        \draw[step=2cm,canvas is yz plane at x=0] (0,0) grid (8,8);
            \node[fill=red] at (-4.08,-2.09) {};
            \node[fill=white] at (-4.08,-.09) {};
            \node[fill=blue] at (-4.08,1.91) {};
            \node[fill=red] at (-4.08,3.91) {};
        \begin{scope}[shift={(-2,0)}]
            \node[fill=blue] at (-4.08,-2.09) {};
            \node[fill=white] at (-4.08,-.09) {};
            \node[fill=orange] at (-4.08,1.91) {};
            \node[fill=white] at (-4.08,3.91) {};
        \end{scope}
        \begin{scope}[shift={(-4,0)}]
            \node[fill=yellow] at (-4.08,-2.09) {};
            \node[fill=blue] at (-4.08,-.09) {};
            \node[fill=white] at (-4.08,1.91) {};
            \node[fill=green] at (-4.08,3.91) {};
            \begin{scope}[shift={(-2,0)}]
                \node[fill=white] at (-4.08,-2.09) {};
                \node[fill=red] at (-4.08,-.09) {};
                \node[fill=blue] at (-4.08,1.91) {};
                \node[fill=yellow] at (-4.08,3.91) {};
            \end{scope}
        \end{scope}
        \draw[xshift=-8cm,yshift=8cm,step=2cm,canvas is xz plane at y=0] (0,0) grid (8,8);
            \draw[fill=yellow,canvas is yz plane at x=0] (0,0) rectangle (2,2);
            \draw[yshift=2cm,fill=blue,canvas is yz plane at x=0] (0,0) rectangle (2,2);
            \draw[yshift=6cm,fill=orange,canvas is yz plane at x=0] (0,0) rectangle (2,2);
        \begin{scope}[shift={(-.77,-.77)}]
            \draw[fill=green,canvas is yz plane at x=0] (0,0) rectangle (2,2);
            \draw[yshift=2cm,fill=orange,canvas is yz plane at x=0] (0,0) rectangle (2,2);
            \draw[yshift=4cm,fill=orange,canvas is yz plane at x=0] (0,0) rectangle (2,2);
            \draw[yshift=6cm,fill=blue,canvas is yz plane at x=0] (0,0) rectangle (2,2);
        \end{scope}
        \begin{scope}[shift={(2*-.77,2*-.77)}]
            \draw[fill=red,canvas is yz plane at x=0] (0,0) rectangle (2,2);
            \draw[yshift=2cm,fill=yellow,canvas is yz plane at x=0] (0,0) rectangle (2,2);
            \draw[yshift=4cm,fill=red,canvas is yz plane at x=0] (0,0) rectangle (2,2);
            \draw[yshift=6cm,fill=red,canvas is yz plane at x=0] (0,0) rectangle (2,2);
        \end{scope}
        \begin{scope}[shift={(3*-.77,3*-.77)}]
            \draw[fill=blue,canvas is yz plane at x=0] (0,0) rectangle (2,2);
            \draw[yshift=2cm,fill=orange,canvas is yz plane at x=0] (0,0) rectangle (2,2);
            \draw[yshift=4cm,fill=yellow,canvas is yz plane at x=0] (0,0) rectangle (2,2);
            \draw[yshift=6cm,fill=blue,canvas is yz plane at x=0] (0,0) rectangle (2,2);
        \end{scope}
            \draw[yshift=8cm,xshift=-2cm,fill=blue,canvas is xz plane at y=0] (0,0) rectangle (2,2);
            \draw[yshift=7.23cm,xshift=-2.76cm,fill=orange,canvas is xz plane at y=0] (0,0) rectangle (2,2);
            \draw[yshift=6.46cm,xshift=-3.55cm,fill=green,canvas is xz plane at y=0] (0,0) rectangle (2,2);
        \begin{scope}[shift={(-2,0)}]
            \draw[yshift=8cm,xshift=-2cm,fill=green,canvas is xz plane at y=0] (0,0) rectangle (2,2);
            \draw[yshift=7.23cm,xshift=-2.76cm,fill=white,canvas is xz plane at y=0] (0,0) rectangle (2,2);
            \draw[yshift=6.46cm,xshift=-3.55cm,fill=red,canvas is xz plane at y=0] (0,0) rectangle (2,2);
            \draw[yshift=5.68cm,xshift=-4.33cm,fill=red,canvas is xz plane at y=0] (0,0) rectangle (2,2);
        \end{scope}
        \begin{scope}[shift={(-4,0)}]
            \draw[yshift=8cm,xshift=-2cm,fill=yellow,canvas is xz plane at y=0] (0,0) rectangle (2,2);
            \draw[yshift=7.23cm,xshift=-2.76cm,fill=yellow,canvas is xz plane at y=0] (0,0) rectangle (2,2);
            \draw[yshift=6.46cm,xshift=-3.55cm,fill=green,canvas is xz plane at y=0] (0,0) rectangle (2,2);
            \draw[yshift=5.68cm,xshift=-4.33cm,fill=red,canvas is xz plane at y=0] (0,0) rectangle (2,2);
        \end{scope}
        \begin{scope}[shift={(-6,0)}]
            \draw[yshift=8cm,xshift=-2cm,fill=green,canvas is xz plane at y=0] (0,0) rectangle (2,2);
            \draw[yshift=7.23cm,xshift=-2.76cm,fill=red,canvas is xz plane at y=0] (0,0) rectangle (2,2);
            \draw[yshift=6.46cm,xshift=-3.55cm,fill=yellow,canvas is xz plane at y=0] (0,0) rectangle (2,2);
            \draw[yshift=5.68cm,xshift=-4.33cm,fill=red,canvas is xz plane at y=0] (0,0) rectangle (2,2);
        \end{scope}
        \begin{scope}[yshift=-4cm]
            \fill[black,canvas is zy plane at x=0] (0,0) rectangle (1.5,1.5);
            \fill[xshift=-2.05cm,yshift=-.58cm] (0,0) rectangle (1.5,1.5);
            \fill[xshift=-1.5cm,yshift=1.49cm,canvas is zx plane at y=0] (0,0) rectangle (1.5,1.5);
                \fill[rounded corners=5,blue,canvas is zy plane at x=0] (0,0) rectangle (1.5,1.5);
                \fill[rounded corners=5,xshift=-2.05cm,yshift=-.58cm,red] (0,0) rectangle (1.5,1.5);
                \fill[rounded corners=5pt,xshift=-1.5cm,yshift=1.49cm,canvas is zx plane at y=0,white] (0,0) rectangle (1.5,1.5);
            \node[fill=white,inner sep=0pt,draw=white] (n) at (-1.3,-1.7) {Another style};
            \draw[line width=1pt,->] (n) --+ (0,1);
        \end{scope}
    \end{tikzpicture}
\end{document}

Here is the original picture:

And the output:

Best Answer

For your first question, a very simple example of how the tikz-3dplot handles its coordinate changes. Note the \tplotsetmaincoords{<angle>}{<angle>} command that sets the view.

I trust you'll be able to add the colors.

\documentclass[border=5pt,tikz]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d}
\begin{document}
    \foreach \myPsi in {90,100,...,170}{
    \tdplotsetmaincoords{70}{\myPsi}
    \begin{tikzpicture}
        \clip (-8,-6) rectangle (8,6);
        \begin{scope}[tdplot_main_coords]
            \draw[step=2cm,canvas is yz plane at x=4] (-4.01,-4.01) grid (4,4);
            \draw[step=2cm,canvas is xz plane at y=4] (-4.01,-4.01) grid (4,4);
            \draw[step=2cm,canvas is yx plane at z=4] (-4.01,-4.01) grid (4,4);
        \end{scope}
    \end{tikzpicture}
    }
\end{document}

Edit
This is bit more realistic with rounded corners:

\documentclass[border=5pt,tikz]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d}
\begin{document}
    \pgfmathsetmacro\radius{0.1}
    \foreach \frontcolor [remember=\frontcolor as \sidecolor (initially blue)] in {red,white,orange,blue}{
        \foreach \myPsi in {90,100,...,170}{
            \tdplotsetmaincoords{70}{\myPsi}
            \begin{tikzpicture}[line join=round]
                \clip (-3,-2.5) rectangle (3,2.5);
                \begin{scope}[tdplot_main_coords]
                    \filldraw [canvas is yz plane at x=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
                    \filldraw [canvas is xz plane at y=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
                    \filldraw [canvas is yx plane at z=1.5] (-1.5,-1.5) rectangle (1.5,1.5);
                    \foreach \X in {-1.5,-0.5,0.5}{
                        \foreach \Y in {-1.5,-0.5,0.5}{
                            \draw [canvas is yz plane at x=1.5,shift={(\X,\Y)},fill=\sidecolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                            \draw [canvas is xz plane at y=1.5,shift={(\X,\Y)},fill=\frontcolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                            \draw [canvas is yx plane at z=1.5,shift={(\X,\Y)},fill=green!60!black] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                        }
                    }
                \end{scope}
            \end{tikzpicture}
        }
    }
\end{document}

Edit 2
As per request, rotating one row:

The code becomes increasingly complex, and drawing order is very important.

\documentclass[border=5pt,tikz]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d}
\begin{document}
    \pgfmathsetmacro\radius{0.1}
    \foreach \frontcolor [remember=\frontcolor as \sidecolor (initially blue)] in {red,white,orange,blue}{
        \foreach \myPsi in {90,100,...,170}{
            \tdplotsetmaincoords{70}{100}
            \begin{tikzpicture}[line join=round]
                \clip (-3,-2.5) rectangle (3,2.5);
                \begin{scope}[tdplot_main_coords]
                    \filldraw [canvas is yz plane at x=1.5] (-1.5,-1.5) rectangle (1.5,0.5);
                    \filldraw [canvas is xz plane at y=1.5] (-1.5,-1.5) rectangle (1.5,0.5);
                    \filldraw [canvas is yx plane at z=0.5] (-1.5,-1.5) rectangle (1.5,1.5);
                    \foreach \X in {-1.5,-0.5,0.5}{
                        \foreach \Y in {-1.5,-0.5}{
                            \draw [canvas is yz plane at x=1.5,shift={(\X,\Y)},fill=blue] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                            \draw [canvas is xz plane at y=1.5,shift={(\X,\Y)},fill=red] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                        }
                    }
                    \tdplotsetrotatedcoords{0}{0}{-\myPsi+90}
                    \begin{scope}[tdplot_rotated_coords]
                        \foreach \X in {-1.5,-0.5,0.5}{
                            \filldraw [canvas is yz plane at x=1.5,shift={(\X,0.5)}] (0,0) rectangle (1,1);
                            \filldraw [canvas is xz plane at y=1.5,shift={(\X,0.5)}] (0,0) rectangle (1,1);
                            \draw [canvas is yz plane at x=1.5,shift={(\X,0.5)},fill=\sidecolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                            \draw [canvas is xz plane at y=1.5,shift={(\X,0.5)},fill=\frontcolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                            \foreach \Y in {-1.5,-0.5,0.5}{
                                \filldraw [canvas is yx plane at z=1.5,shift={(\X,\Y)}] (0,0) rectangle (1,1);
                                \draw [canvas is yx plane at z=1.5,shift={(\X,\Y)},fill=green!60!black] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                            }
                        }
                    \end{scope}
                \end{scope}
            \end{tikzpicture}
        }
    }
\end{document}

To get it to rotate back and forth I cheated a bit when converting it to a .gif:

Edit 3
This pretty much makes you able to control the rotation with buttons:

\documentclass[]{article}
\usepackage{animate}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d}

\newwrite\OutFile%
\immediate\openout\OutFile=tl.txt%
\immediate\write\OutFile{::0x0,1}
\foreach \i in {2,...,36}{
    \immediate\write\OutFile{::\i}%
}
\immediate\closeout\OutFile


\pgfmathsetmacro\radius{0.1}
\tdplotsetmaincoords{70}{100}

\newcommand{\drawRotatedRow}[2][2]{
    \pgfmathsetmacro\myHeight{-1.5+int(#1)}
    \pgfmathsetmacro\myPsi{#2}
    \pgfmathsetmacro\mySecondPsi{-80+Mod(\myPsi+80,90)}
    \pgfmathtruncatemacro\mySegment{Mod((\myPsi+80)/90,4)}
    \ifcase\mySegment% segment 0
        \def\frontcolor{red}
        \def\sidecolor{blue}
    \or% segment 1
        \def\frontcolor{blue}
        \def\sidecolor{orange}
    \or% segment 2
        \def\frontcolor{orange}
        \def\sidecolor{white}
    \or% segment 3
        \def\frontcolor{white}
        \def\sidecolor{red}
    \fi
    \begin{scope}[tdplot_main_coords]
        \tdplotsetrotatedcoords{0}{0}{\mySecondPsi}
        \begin{scope}[tdplot_rotated_coords]
            \filldraw [canvas is yx plane at z={\myHeight+1}] (-1.5,-1.5) rectangle (1.5,1.5);
            \filldraw [canvas is yz plane at x=1.5] (-1.5,\myHeight) rectangle (1.5,{\myHeight+1});
            \filldraw [canvas is xz plane at y=1.5] (-1.5,\myHeight) rectangle (1.5,{\myHeight+1});
            \foreach \X in {-1.5,-0.5,0.5}{
                \draw [canvas is yz plane at x=1.5,shift={(\X,\myHeight)},fill=\sidecolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                \draw [canvas is xz plane at y=1.5,shift={(\X,\myHeight)},fill=\frontcolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                \ifnum#1=2\relax
                    \foreach \Y in {-1.5,-0.5,0.5}{
                        \draw [canvas is yx plane at z={\myHeight+1},shift={(\X,\Y)},fill=green!60!black] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                    }
                \fi
            }
        \end{scope}
    \end{scope}
}
\begin{document}
    \begin{animateinline}[controls,loop,timeline=tl.txt]{10}
        \begin{tikzpicture}[line join=round]
            \clip (-3,-2.5) rectangle (3,2.5);
            \drawRotatedRow[0]{0}
            \drawRotatedRow[1]{0}
        \end{tikzpicture}
        \newframe
        \multiframe{36}{iPsi=0+10}{%
            \begin{tikzpicture}[line join=round]
                \clip (-3,-2.5) rectangle (3,2.5);
                \drawRotatedRow{\iPsi}
            \end{tikzpicture}
        }
    \end{animateinline}
\end{document}

I added a command that draws a row of cubes, with optional z level (defaults to 2, zero based) and with a rotation about z: \drawRotatedRow[<level>]{<rotation>}. With this command now we can do something like this:

\documentclass[tikz]{standalone}
\usepackage{animate}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d}

\pgfmathsetmacro\radius{0.1}
\tdplotsetmaincoords{70}{100}

\newcommand{\drawRotatedRow}[2]{
    \pgfmathsetmacro\myHeight{-1.5+int(#1)}
    \pgfmathsetmacro\myPsi{#2}
    \pgfmathsetmacro\mySecondPsi{-80+Mod(\myPsi+80,90)}
    \pgfmathtruncatemacro\mySegment{Mod((\myPsi+80)/90,4)}
    \ifcase\mySegment% segment 0
        \def\frontcolor{red}
        \def\sidecolor{blue}
    \or% segment 1
        \def\frontcolor{blue}
        \def\sidecolor{orange}
    \or% segment 2
        \def\frontcolor{orange}
        \def\sidecolor{white}
    \or% segment 3
        \def\frontcolor{white}
        \def\sidecolor{red}
    \fi
    \begin{scope}[tdplot_main_coords]
        \tdplotsetrotatedcoords{0}{0}{\mySecondPsi}
        \begin{scope}[tdplot_rotated_coords]
            \filldraw [canvas is yx plane at z={\myHeight+1}] (-1.5,-1.5) rectangle (1.5,1.5);
            \filldraw [canvas is yz plane at x=1.5] (-1.5,\myHeight) rectangle (1.5,{\myHeight+1});
            \filldraw [canvas is xz plane at y=1.5] (-1.5,\myHeight) rectangle (1.5,{\myHeight+1});
            \foreach \X in {-1.5,-0.5,0.5}{
                \draw [canvas is yz plane at x=1.5,shift={(\X,\myHeight)},fill=\sidecolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                \draw [canvas is xz plane at y=1.5,shift={(\X,\myHeight)},fill=\frontcolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                \ifnum#1=2\relax
                    \foreach \Y in {-1.5,-0.5,0.5}{
                        \draw [canvas is yx plane at z={\myHeight+1},shift={(\X,\Y)},fill=green!60!black] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                    }
                \fi
            }
        \end{scope}
    \end{scope}
}
\begin{document}
    \foreach \iPsi in {0,10,...,359}{
        \begin{tikzpicture}[line join=round]
            \clip (-3,-2.5) rectangle (3,2.5);
            \drawRotatedRow{0}{-\iPsi}
            \drawRotatedRow{1}{0}
            \drawRotatedRow{2}{\iPsi}
        \end{tikzpicture}
    }
\end{document}

Or even this (very long GIF):

\documentclass[tikz]{standalone}
\usepackage{animate}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d}

\pgfmathsetmacro\radius{0.1}
\tdplotsetmaincoords{70}{100}

\newcommand{\drawRotatedRow}[2]{
    \pgfmathsetmacro\myHeight{-1.5+int(#1)}
    \pgfmathsetmacro\myPsi{#2}
    \pgfmathsetmacro\mySecondPsi{-80+Mod(\myPsi+80,90)}
    \pgfmathtruncatemacro\mySegment{Mod((\myPsi+80)/90,4)}
    \ifcase\mySegment% segment 0
        \def\frontcolor{red}
        \def\sidecolor{blue}
    \or% segment 1
        \def\frontcolor{blue}
        \def\sidecolor{orange}
    \or% segment 2
        \def\frontcolor{orange}
        \def\sidecolor{white}
    \or% segment 3
        \def\frontcolor{white}
        \def\sidecolor{red}
    \fi
    \begin{scope}[tdplot_main_coords]
        \tdplotsetrotatedcoords{0}{0}{\mySecondPsi}
        \begin{scope}[tdplot_rotated_coords]
            \filldraw [canvas is yx plane at z={\myHeight+1}] (-1.5,-1.5) rectangle (1.5,1.5);
            \filldraw [canvas is yz plane at x=1.5] (-1.5,\myHeight) rectangle (1.5,{\myHeight+1});
            \filldraw [canvas is xz plane at y=1.5] (-1.5,\myHeight) rectangle (1.5,{\myHeight+1});
            \foreach \X in {-1.5,-0.5,0.5}{
                \draw [canvas is yz plane at x=1.5,shift={(\X,\myHeight)},fill=\sidecolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                \draw [canvas is xz plane at y=1.5,shift={(\X,\myHeight)},fill=\frontcolor] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                \ifnum#1=2\relax
                    \foreach \Y in {-1.5,-0.5,0.5}{
                        \draw [canvas is yx plane at z={\myHeight+1},shift={(\X,\Y)},fill=green!60!black] (0.5,0) -- ({1-\radius},0) arc (-90:0:\radius) -- (1,{1-\radius}) arc (0:90:\radius) -- (\radius,1) arc (90:180:\radius) -- (0,\radius) arc (180:270:\radius) -- cycle;
                    }
                \fi
            }
        \end{scope}
    \end{scope}
}
\begin{document}
    \foreach \level in {0,1,2}{
        \foreach \iPsi in {0,10,...,359}{
            \begin{tikzpicture}[line join=round]
                \clip (-3,-2.5) rectangle (3,2.5);
                \ifcase\level % Level 0 rotating
                    \drawRotatedRow{0}{\iPsi}
                    \drawRotatedRow{1}{0}
                    \drawRotatedRow{2}{0}
                \or % Level 1 rotating
                    \drawRotatedRow{0}{0}
                    \drawRotatedRow{1}{\iPsi}
                    \drawRotatedRow{2}{0}
                \or % Level 2 rotating
                    \drawRotatedRow{0}{0}
                    \drawRotatedRow{1}{0}
                    \drawRotatedRow{2}{\iPsi}
                \fi
            \end{tikzpicture}
        }
    }
\end{document}

Related Solutions

[Tex/LaTex] Rotate a node but not its content: the case of the ellipse decoration

The source of the difficulty is that ellipses are constructed in a particular way in TikZ. They are paths that start from the x-axis and proceed counter-clockwise around their centre. The vast majority of the time, the exact parametrisation doesn't matter. You appear to have found the one situation where it does!

In the actual question, you only want to be able to mirror the ellipse, and so draw it starting from the negative x-axis (the title of the question suggests a more flexible approach). That's actually not too hard since we can exploit the symmetry of the ellipse. The key is to provide it with a negative x-radius, since then it will start from the negative x-axis (and proceed clockwise, but we could correct for that by negating the y-radius as well). To do this, we interrupt the call from the node shape to the drawing command and flip the sign of the x-radius. The simplest way to do this is to redefine the \pgfpathellipse macro to do the negation and then call the original macro. The following code does this.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations,shapes,decorations.markings}
\makeatletter
\let\origpgfpathellipse=\pgfpathellipse
\def\revpgfpathellipse#1#2#3{%
  #2%
  \pgf@xa=-\pgf@x
  \origpgfpathellipse{#1}{\pgfqpoint{\pgf@xa}{0pt}}{#3}}
\makeatother

\tikzset{
  reversed ellipse/.style={
    ellipse,
    reverse the ellipse%
  },
  reverse the ellipse/.code={
    \let\pgfpathellipse=\revpgfpathellipse
  }
}
\begin{document}
\begin{tikzpicture}
\node[ellipse,
  draw,
  postaction={
    decorate,
    decoration={
      markings,
      mark=at position 1 with {
        \arrow[line width=5pt,blue]{>}
      }
    }
  }
] at (0,0) {hello world};

\node[reversed ellipse,
  draw,
  postaction={
    decorate,
    decoration={
      markings,
      mark=at position 1 with {
        \arrow[line width=5pt,blue]{>}
      }
    }
  }
] at (0,-2) {hello world};
\end{tikzpicture}

\end{document}

Here's the result:

rotated ellipse

(the arrow got clipped, but you can see where it lies)

[Tex/LaTex] How to fix the trajectory of Brownian motions which generated by the “rand” function with tikz in beamer frames

First a few remarks:

the \foreach loop assumes a difference of one between elements if only a start and end are connected via dots, so \foreach \x in {1,2,...,100} will yield the same as \foreach \x in {1,...,100}
you paint white over over your RONI (region of no interest). It is better to \clip the ROI (region of interest)
using beamer commands in a TikZ-picture did not seem to work propperly, so I used the \only<n> specifivation to show the entire pictures on different slides
while you and me might get from {1,...,7} that the numbers are supposed to be integers, computers don't neccessarily, thats why I converted the outer for-loop variable (\f) to an interger (\i) via \pgfmathtruncatemacro
the \scope is used to keep the clipping local

And here's the result:

\documentclass{beamer}
\useoutertheme{infolines}
\usetheme{Darmstadt}
\usepackage{tikz}
\begin{document}

\begin{frame}{Brownian motions}
    \foreach \f in {1,...,7}
    {   \pgfmathtruncatemacro{\i}{\f}
      \only<\i>{\begin{tikzpicture}[scale=0.55]
        \draw[help lines] (0,0) grid (15,10);

            \begin{scope}
            \clip (0,0) rectangle (15,\i+3);
                \draw[red] (0,0)
            \foreach \x in {1,...,750}
              { -- ++(0.02,rand*0.2+0.01) };
            \draw[blue] (0,0)
            \foreach \x in {1,...,750}
              { -- ++(0.02,rand*0.2+0.01) };
            \draw[green] (0,0)
            \foreach \x in {1,...,750}
              { -- ++(0.02,rand*0.2+0.01) };
            \draw[orange] (0,0)
            \foreach \x in {1,...,750}
              { -- ++(0.02,rand*0.2+0.01) };
            \end{scope}

      \draw[thick,red] (0,\i+3) -- ++(15,0);
        \draw[thick,->,>=stealth] (0,0) -- (16,0) node[right] {$t$};
        \draw[thick,->,>=stealth] (0,0) -- (0,11) node[above] {$Y_t$};
      \end{tikzpicture}}
    }   
\end{frame}

\end{document}

enter image description here

For putting certain plots only on some slides, you could use the \ifthenelse{condition}{true path}{false path} command from the xifthen package:

\documentclass{beamer}
\useoutertheme{infolines}
\usetheme{Darmstadt}
\usepackage{tikz}
\usepackage{xifthen}

\begin{document}

\begin{frame}%{Brownian motions}
  \foreach \f in {1,...,7}
  { \pgfmathtruncatemacro{\i}{\f}
    \only<\i>{
        \begin{tikzpicture}[scale=0.55]
            \draw[help lines] (0,0) grid (15,10);
          \begin{scope}
            \clip (0,0) rectangle (15,\i+3);
            \draw[blue] (0,0)
              \foreach \x in {1,...,750}
              { -- ++(0.02,rand*0.2+0.01) };
                    \ifthenelse{\i<7}
                    {   \draw[red] (0,0)
                \foreach \x in {1,...,750}
                { -- ++(0.02,rand*0.2+0.01) };
                \draw[green] (0,0)
                \foreach \x in {1,...,750}
                { -- ++(0.02,rand*0.2+0.01) };
                \draw[orange] (0,0)
                \foreach \x in {1,...,750}
                { -- ++(0.02,rand*0.2+0.01) };
              }{}  
          \end{scope}
          \draw[thick,red] (0,\i+3) -- ++(15,0);
          \draw[thick,->,>=stealth] (0,0) -- (16,0) node[right] {$t$};
          \draw[thick,->,>=stealth] (0,0) -- (0,11) node[above] {$Y_t$};
        \end{tikzpicture}
    }
  }
\end{frame}

\end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] Rotate a node but not its content: the case of the ellipse decoration

[Tex/LaTex] How to fix the trajectory of Brownian motions which generated by the “rand” function with tikz in beamer frames

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