Spirographs

[MattSchultz]

Spirographs, or rather, cycloids, have always fascinated me.

When I was in highschool, I got out of a math project (which was to write a poem about math) by deriving the equations for a hypocycloid and using those equations to produce a Spirograph generator, which, sadly, is long-since lost. The generator was fairly complete, going as far as to include a simply macro language for the generation of successive cycloid images. I used the software to produce several images, only one of which remains, and only in print form (I'll try to scan it later), but it was quite neat in its day.

I'm interested in potentially re-visiting the generator, as I now can derive the equations quite quickly and the program would be fairly simple to re-do. I'm wondering what the community interest in such a generator might be, and if there are any requests. The original generator could handle only a small set of parameters, but I'm giving some thought to trying to get it to do more, including epicycloid drawing and perhaps even custom shapes using collision detection. If I did this, what would you guys like to see? The project would probably be done with WPF. How many of you use a Mac? If there is enough demand for it, I may do it as a browser-based Silverlight application, allowing it to run on Windows, Mac, or Linux.

What do you all think?

-ps Spirograph is a registered, but poorly enforced, trademark of Hasbro. The proper name for a spirograph is a cycloid. Since nobody knows what a cycloid is, however, I often use Spirograph instead. Sue me.

[cKleinhuis]

do you mean those ?
http://mathworld.wolfram.com/Cycloid.html

hmm, i wonder how you do nice images with that method, using a spline to define the path along the circle rolls ?

[Sockratease]

hmm, i wonder how you do nice images with that method, using a spline to define the path along the circle rolls ?

These are the idea behind guilloche designs (the "Security" patterns on money, etc).

Here's a program that takes the concept to the limits!

http://www.excourse.com/excentro/

Got the trial for the mac - it's a Wonderful Program!!  (So Yes, I use a mac as well as a PC)

If you can do things like that...  You'll have a hit on your hands!

[MattSchultz]

Trifox - yes. Commonly, however, spirographs are what is called hypocycloids, which are produced the same way, except the circle is rolling inside another circle. The end result is a very cool image.

Here is a typical (partial) image:

http://monicarivella.files.wordpress.com/2007/12/circleproject02.jpg

I'm going to scan the one I have, when I'm done, I'll put it on my flickr feed. It is quite unique, I've found nothing like it since (though it is a hypocycloid it was heavily altered, but still looks cool).

[edit]

As for how to do it - The original version rendered the image. By rendering, I mean directly simulated its creation. It had a mode where you could even watch it draw the image. The best solution would be to directly vectorize it, but, being a non-math/spline/beizer guy, I don't really know how, and I don't think I'm going to bother to learn.

I don't actually think guilloche designs are usually cycloidic, but I suppose some may be.

My scanner is going. At 1200DPI, however, it takes 30 minutes to finish, so it will be some time before I can get the image up (plus I still have to clean and fix it)....

...Working on cleaning image now, got distracted by making stupid hippie stuff for room...

[cKleinhuis]

well well, if i figure it out how it is done i will use it in a forthcoming demo 

[MattSchultz]

...Finally finished picture (and stupid hippie stuff!)

http://www.flickr.com/photos/abstractapproach/2541242400/

It is apparent that it is a Spirograph (yes generated not hand drawn) but it was MASSIVELY edited, and so barely resembles it's original design. Granted, there were some 80 separate traces on this image alone, making it fairly complex in its own right.

[seconteen]

oh boy i remember these. I used to have a pocket spirograph thingy... it wasn't that good cus the paper wouldn't stay in place. I still have it somewhere but I'm pretty sure some of the pieces are missing.

[jehovajah]

If you want the real deal download these.

Unfortunately try as i might i cannot get Laz to communicate!!

Maybe somebody here might help me to talk to him.

By the way spirographs, roulettes are fundamental to Fractal art and all fractals. I might even say: to the description of the workings of our universe from quantum to cosmological scales.

[jehovajah]

r(t)=cos(t)^1+sin(t)^2
theta(t)=t*10

Try these here and the polar coordinates.

Use t*n for n= 1,2,3,4,5,6,7,8...etc. for theta(t)  and various positive powers for r(t).

[ant123]

I had a spirograph too!!!, i forgot how fun they are. ...not as exciting as lego, if only they had made a spirograph kit out of lego.

http://blogs.msdn.com/b/socaldevgal/archive/2008/12/13/spirographs.aspx

That program excentro is AWESOME. Very nice, looks like banknotes.

the easiest thing to do in maths as it consists of a sine wave, or a sine and cosine, operating at different speeds, like the cosine does one turn for every 10-20 turns of the sine. that just makes round flower shapes, i dont know how to do the triangles off hand. but if you get sines and cosines and make frills that slowly migrate across the page you have excentro.

you could program them yourself in the free version of reaktor if there is a free version, that lets u program i dont know, using the XY module, sines and cosines. set the XY to 100 fade time.
ese you need a program that can add and trace sine and cosine graphs, circles etc.

[jehovajah]

It is fascinating. I got one for my birthday recently! It is hard to easily get the old style.
Love the pic on your site. Nice!

[lkmitch]

If you use Ultra Fractal, there's a spirograph coloring by Ken Childress (based on work by Sam Monier).  I've done guilloche colorings and an elliptical spirograph, but haven't gotten around to publishing them.  Here is one of my guilloche images; I call it "Vitruvian Man," after Leonardo's sketch.

[alinta]

Sorry to pull up something old, but have users on this forum of the Excentro program been using the full version or the lite version? Just looking for some reviews of the lite version - hoping to not have to commit to the full version.

Cheers
Alinta