I made a geogebra thingy to try and illustrate time dilation. Hopefully this link will work:

https://www.geogebra.org/m/xXE5SheR
This has a slider v but you need to scroll about half way down to see it. It was supposed to represent velocity but because I got confused about the time axis pointing upwards it ended up representing the reciprocal of velocity. Anyway changing the velocity changes the hyperbola axis intercepts which I am imagining is showing time dilation.

To calculate the hyperbola axis intersections I used the following calculations:

https://gist.github.com/kiwiheretic/...b072379454967c
I am a little confused as to why I got $\displaystyle \frac{v}{\sqrt{v^2-1}}$ as that part doesn't look right but it does produce the expected outcome of the tangent lines of the hyperbola intersecting the axiswhich is the way that Peter Collier seem to do it (see attachment) except that I scaled the hyperbola so that their tangent lines intersected the axis at integral positions of 1,2,3, ... . (I was trying to figure out how a moving observers co-ordinate grid maps to a stationary observers co-ordinate grid at the time.)

Or am I doing something wrong?