So I found THIS video on YouTube (you should REALLY check it out!). It explains how a children toy works how it is able to draw pretty pictures with a simple mechanism. The video also explains how the mechanism works and the derives the formula for the function that represents the graph at the end. I wanted to do the same, but with pure simulation. So I sat down for a day and programmed this little thing you see on top of the screen in Unity.
You will first need a base knowledge of what is going on screen.
1) Select Nr of circles to be 2
2) Click simulate.
You can now see how the outer circle moves around the inner one, drawing a line at the end of a line.
If you tinker with the circle radius or the line length, you can see how the drawing changes (use clear canvas if needed)
You can see that a simulation speed of 100 is quite slow, so you may bump up the value there, but be careful as higher simulation
speeds in "slow mode" (I will explain that soon, promise) as that will impact accuracy of the spiral.
Now that we understand how the spirals are created, let's create them faster.
!!! TRIGGER WARNING FOR PEOPLE THAT CAN'T DEAL WITH FLASHING IMAGES, FAST MODE WITH ANIMATION WILL HAVE FLASHING IMAGES !!!
Untick the box that says "use slow mode".
You can now see the simulation of the spiral with simulation speed steps (so 1000 for example).
This allows us to visualize the spiral quicker.
Now play with the sliders and have fun :)
This thing is just too mesmerizing for me and I've been playing with it for like 5 hours already.
Please reach me at firstname.lastname@example.org if you want to get in touch.