There has been a lot of people that get lost when they read my description of the spirograph.
Here there is a tutorial that could help you to get totally lost. (just kidding :-)
The first thing you have to understand is that the disc number, and the ring number are the radii of the gears.
The number of leaves or peaks that a spirogram has, depends on these numbers. The relation between them is this:
number_of_peaks = lcm(ring,disc) / disc
Here, lcm, stands for: least common multiple.
v. gr. if you have ring=100, disc=60, then you get an spirogram with 5 peaks (or leaves). Because the least common multiple of 100 and 60 is 300, divided by 60 yields 5.
So, lets try to make a 5 peaks star with the spirograph.
1. Let us set:
These changes will make us have only one cycle and the spirogram we are going to draw will be white.
2. Set the main parameters:
3. Lets forget the increments for a while.
4. Trace the spirogram.
Ladies and Gentlemen, a brand new star!!!5. Now, let us change the hole
6. Trace the spirogram.
...and we get the same star, but now the peaks are softer.
Now, let us make several spirograms in a single sketch. In this sketch we are going to change the value of hole. Each cycle draws a closed spirogram so, let us understand that we are going to make an increment on the value of hole each time a cycle is completed.
8. Trace the spirogram.
... and we get a cushion star with 5 peaks...
Easy, isn't it? When you make a cycle, all the parameters are changed according to the increment you specify.
Another parameter that is important to understand is the deviation. Let us return to the parameters...
10. Trace the spirogram.
Perhaps you have noticed that the star is now rotated 20 degrees...
12. Trace the spirogram.
You will see now 10 stars. Each of them is rotated, the rotation angles go from 0 to 27 degrees...
And, what about changing both parameters at the same time ? I mean, change hole and deviation. Let us do it.
14. Trace the spirogram.
Interesting, isn't it ?
There are many other posibilities.
You can use negative discs, this will make the disc roll outside the ring.
You can change the color, using increments. As I explained in the main page, the pen's color is composed by 3 elements: Red Green Blue and they are specified in a 6 digit hexadecimal number.
Spirograms are created approximating the curve by a connected set of straight lines. The number of lines that are used for aproximating one round of the disc around the ring is given by resolution The more resolution, the finer sketch. Try to play with this parameter...
Again, a beautiful sketch, not so soft as the ones we made, but it is beautiful anyway.