Cfrgtkky

Here's a quick visual link to what I want to show,

https://www.youtube.com/watch?v=rVvGqWyQB_0&index=2&list=PL5563BAB9EA968641

at 6:09.

I've tried using minipages but that won't allow for a line to go from one plot to the other and here is the code for one of the plots,

begin{tikzpicture}

begin{axis}[ 

ticks=none,

axis lines = middle,

axis line style={->},

ymin=-0.5, ymax = 2.5,

xmin=-0.5, xmax=2.5,

xlabel={$x$},

ylabel={$y$},

axis equal image

]

draw (axis cs:1.25,1.25) circle [blue, radius=0.5];

draw[color=blue] (axis cs:1.25,1.25) node[above left] {$a$};

draw[color=blue] (axis cs:1.25,1.25) node{$bullet$};

draw [->] (axis cs:1.25,1.25)  -- node[pos = 0.5, below] {$delta$} (axis cs:1.75,1.25) ;



end{axis}

end{tikzpicture}

It is possible to create several axis environments and shift them with xshift.
Then, simply draw an arrow from one to the other.

documentclass{article}

usepackage{tikz,pgfplots}





begin{document}

begin{tikzpicture}

begin{axis}[ 

ticks=none,

axis lines = middle,

axis line style={->},

ymin=-0.5, ymax = 2.5,

xmin=-0.5, xmax=2.5,

xlabel={$x$},

ylabel={$y$},

axis equal image

]

draw (axis cs:1.25,1.25) circle [blue, radius=0.5];

draw[color=blue] (axis cs:1.25,1.25) node[above left] {$a$};

draw[color=blue] (axis cs:1.25,1.25) node (a) {$bullet$};

draw [->] (axis cs:1.25,1.25)  -- node[pos = 0.5, below] {$delta$} (axis cs:1.75,1.25) ;



end{axis}



begin{axis}[ xshift=7cm,

ticks=none,

axis lines = middle,

axis line style={->},

ymin=-0.5, ymax = 2.5,

xmin=-0.5, xmax=2.5,

xlabel={$x$},

ylabel={$y$},

axis equal image

]

draw (axis cs:1.25,1.25) circle [blue, radius=0.5];

draw[color=blue] (axis cs:1.25,1.25) node[above] {$a$};

draw[color=blue] (axis cs:1.25,1.25) node(b){$bullet$};

draw [->] (axis cs:1.25,1.25)  -- node[pos = 0.5, below] {$delta$} (axis cs:1.75,1.25) ;



end{axis}



draw[->](a)to[bend left](b);

end{tikzpicture}

end{document}

In the video it seems that the points also get accessed from outside, which means you might need remember picture anyway.

documentclass{article}

usepackage{tikz}

usepackage{pgfplots}

pgfplotsset{compat=1.16}

usetikzlibrary{tikzmark}

begin{document}

begin{figure}[htb]

centering

begin{tikzpicture}[remember picture]

begin{axis}[ 

ticks=none,

axis lines = middle,

axis line style={->},

ymin=-0.5, ymax = 2.5,

xmin=-0.5, xmax=2.5,

xlabel={$x$},

ylabel={$y$},

axis equal image

]

draw (axis cs:1.25,1.25) circle [blue, radius=0.5];

draw[color=blue] (axis cs:1.25,1.25) node[above left] {$a$};

draw[color=blue] (axis cs:1.25,1.25) node{$bullet$};

draw [->] (axis cs:1.25,1.25)  -- node[pos = 0.5, below] {$delta$} (axis cs:1.75,1.25) 

coordinate(d1);

end{axis}

end{tikzpicture}

quad

begin{tikzpicture}[remember picture]

begin{axis}[ 

ticks=none,

axis lines = middle,

axis line style={->},

ymin=-0.5, ymax = 2.5,

xmin=-0.5, xmax=2.5,

xlabel={$x$},

ylabel={$y$},

axis equal image

]

draw (axis cs:1.25,1.25) circle [blue, radius=0.5];

draw[color=blue] (axis cs:1.25,1.25) node[above left] {$a$};

draw[color=blue] (axis cs:1.25,1.25) node{$bullet$};

draw [->] (axis cs:1.25,1.25)  -- node[pos = 0.5, right] {$delta$} 

(axis cs:1.25,0.75) coordinate(d2);

end{axis}

end{tikzpicture}

caption{On the left, our point is on the

tikzmarknode{D1}{right} while it is on the tikzmarknode{D2}{bottom} in the

right figure. }

begin{tikzpicture}[overlay,remember picture]

draw[red,-latex] (D1) to[out=90,in=-90] (d1);

draw[red,-latex] (D2) to[out=90,in=-90] (d2);

draw[red,-latex] (d1) to[out=0,in=180] node[midway,above,sloped,fill=white,fill

opacity=0.6]{has moved}(d2);

end{tikzpicture}

end{figure}

end{document}