I am working on overleaf and I want to make a diagram to represent the ordinal numbers (a mathematical term) in the following way…
I am using tikzpicture
to make this diagram. My attempt is as follows (not completed!).
\begin{tikzpicture}
\draw[gray] (-4,-4) grid (4,4);
\draw (0,0) node[] {$0$};
\draw (-0.3,-0.2) node[] {$1$};
\draw (-0.5,-0.4) node[] {$2$};
\draw (-0.4,-0.7) node[] {$3$};
\draw[-> , dotted] (-0.3,-0.8) .. controls (0.2,-1.2) and (1,-0.3) .. (0.3,0.4) ;
\draw (0,0.5) node[] {$\omega$};
\draw (-0.8,0.3) node[] {$\omega+1$};
\draw (-1.3,-0.3) node[] {$\omega+2$};
\draw (-1.1,-0.8) node[] {$\omega+3$};
\draw[-> , dotted] (-1,-1) .. controls (-0.9,-1.3) and (-0.6,-1.5) .. (-0.35,-1.5) ;
\draw (0,-1.5) node[] {$2 \cdot \omega$};
\draw[-> , dotted] (.55,-1.5) .. controls (1.2,-1.3) and (1.3,-0.8) .. (1.3,-0.5) ;
\draw (1.3,-0.3) node[] {$3 \cdot \omega$};
\draw[-> , dotted] (1.3,0) .. controls (1.3,0.5) and (1,1.3) .. (0.3,1.3) ;
\draw (0,1.3) node[] {$\omega^{\omega}$};
\end{tikzpicture}
whose output is as follows
But the problem is, it is very time-consuming and is not looking that much beautiful. Also, the entries like $\omega + 1, \omega + 2$, etc are feeling so big in this picture. Can we reduce the size? Can anyone tell me any other way to create such diagrams? any link to check or any source someone provide?
any sort of help will be very helpful.
Note: I am using the grid on purpose to draw the entries accordingly. By beautiful, I did not mean about the grid, I can comment that line.
Thanks in advance.
Best Answer
I found it an interesting challenge, since it is about placing terms in something similar to a spiral, searching I found this very detailed code from Guilherme Zanotelli to draw parametric spirals, and then I adapted it to obtain a similar result, I have used some nesting to place the nodes.
RESULT:
MWE: