Wheel curves 6c / Hjulkurvor 6c
Just press green flag and use TURBO
to see an animation of pattern after pattern of wheel curves.
- k is 11 or 12, (observe the rotational symmetry! Is it k-fold?)
- w1 changes during the animation (Just observe it.)
The animation will go on till you press the red stop button.
Then press v, adjust some variable, press v and green flag again.
- n is the number of curves (1-20)
- s is the scale factor
- pause1 and pause2 determine the speed of the animation
- Four wheels with radii r1-r4, angular velocities w1-w4 and phases ph1-ph4. For rotational symmetry:
w2=w1+ka, w3=w1+kb, w4=w1+kc (k,a,b,c integers), i.e.
the differences between the values of w1-w4 are multiples of k.
- MATHEMATICAL CHALLENGE:
Can you see why the rotational symmetry is not always k-fold?
In the slider I chose to use only k=11 and k=12, because I think that comparing the results for these two values might be helpful.
- See inside and explore the code. I've written some comments hoping that they are useful and that you'll remix to make new animations!
- I like only some of the pictures myself, but decide to share this anyhow. Maybe you will find more interesting examples =)