Discussion
Well. I had a program that drew hyper and hypo cycloids using the turtle but I seem to have misplaced it. Can't find my code anywhere.
But that means I get to write it again, and I could make it better this time.
One thing that bothered me about the old code is I didn't use the unique way that turtles can draw circles, I just used cartesian coordinates and goto commands.
Could there be a more elegant way?
@futurebird The instantaneous velocity of a spirograph is a fairly simple function of time. From memory, the pen is inside a disk. The pen velocity is
disk's center velocity + pen velocity around center.
Tell the turtle to go in that direction.
@futurebird You could imagine the turtle rocking and spinning with the spirograph based on centripital force calculations.
I’d guess you’d need to calculate the second derivative of the hypocycloid. Might be easier in polar coordinates. Then you have the turtle always facing the opposite direction while flailing its arms. The magnitude of the vector should determine the turtle’s tilt.
The turtld isn’t aalking, it’s riding the pen.
@futurebird Used to do these and noires created by interference and pixelated diagonals on the Apple IIe machines all the time. I wonder if I still have hard copy code anywhere... So much fun!
Circle
Repeat 360 times
Forward 1
Left 1
Spiral in here. You change the side length each irritation
https://el.media.mit.edu/logo-foundation/what_is_logo/logo_primer.html
The spirals made with squares look a bit like cycloids, but it's not the same motion as the spirograph.
@futurebird it's frustrating because 14 year old me could actually help. C64 logo Lab aid
@futurebird I doubt it would be especially elegant, but I think for the sake of variety you should use polar co-ordinates with local centers.
(the more I think about this, the harder it seems to make good choices about the locations of the local centers. )
@futurebird This was a problem we worked on using LEGO Robots. On some turtles that have good position or speed feedback on the motors, you can set the speed of the left and right motors independently.
Big circle is left motor slightly different speed than right - have fun and let the kids find out about differential steering!
Hyper/hypo cycloids are the fancy math words for "spirographs"
I guess a first step would be to find a new way of thinking about the sine and cosine curves since I was basically using those functions to calculate the motion of the interlocking circles.
hmmm...
@futurebird That sounds like a fun time. For some reason I'm writing COBOL right now? If I had any self respect at I would immediately stop and go make spirographs with Logo or something, but apparently I enjoy feeling pain lol
I kind of stumbled into teaching middle school CS (didn't want to do it, I thought it'd be boring, I was very wrong) but, in fact, it means part of my job is playing with fun code all day.
Most schools have endless desire to run such classes and no one to teach them.
@futurebird Oh! How delightful. I didn't realize middle schools even had a CS curriculum (well I'm in Canada, so I wouldn't, but I don't know if it's even a thing around here either tbh). That sounds like it'd be an interesting experience.
My CS teacher in grade 9 actually taught me a lot, despite my going into that class mostly just seeking an easy A, lol.
Install Fedizen
Get the full app experience
@futurebird That's how I did it as a teen (although at the time I was using FORTRAN). My math wasn't up to doing it any other way, although I also had fun playing with the - I think it's called - evolute and involute of those curves?