Pen-Dragon Mechanical Fractal-Drawing Device

[aeh5040]

Here is by far my most ambitious project. It is a purely mechanical device which draws a fractal curve, driven by only one motor. So far as I know, this is the first time such a thing has ever been done in any medium, Lego or otherwise! Specifically, it draws a Heighway Dragon Curve, a space-filling curve that never crosses itself. It in fact draws a "twin dragon" which would in principle join up to form a loop, given enough time, floor space, and paper. (In practice, slight inaccuracies mean that it would not quite join up).

I actually made this over a year ago (and it was the result of about a year of hard work), and showed it at BrickCon 2012. The long delay is partly due to the difficulty of filming it!

The "brain" on the top layer consists of a series of Geneva mechanisms. These required many designs to get the motion smooth and precise enough - they also require a 45 degree offset. Each Geneva wheel is connected to two cams, one on the left side, and one on the right. The cams lift the two levers running along the sides in a particular sequence, related to Gray code (a variant of binary counting). When translated to left and right turns, this gives the Dragon Curve. The bottom layer contains two identical mechanisms controlling the two wheels, to enable precise turns. When one side is triggered by a cam, the wheel on that side needs to make exactly one turn. After many failed attempts, I was able to do achieve this using a variant of the "Tomy Armatron" mechanism (which was discussed here before), combined with a Scotch Yoke linkage. A worm drive ensures that the wheels are locked and cannot turn when not triggered.

Enjoy!

Here is what it would theoretically draw, after 256 turns, given enough space:

Edited February 17, 2014 by aeh5040

[JGW3000]

I am totally flabbergasted; so intricately beautiful, clever and unique. Love the concept of a plotter machine running over paper, reminds me of HP plotters from the 1980's - you are using a similar type of pen. Would love to see building instructions or an lxf.

What size paper are you using?

[Gilbert Despathens]

Wow, that's brilliant. Since I've never attempted anything like that, I'm curious - did you plan a machine that could draw the fractal and then find out how to build it with Lego, or did you start with the Lego and build the machine through a system of experiments? If the former was the case as I hesitantly suspect, which part of the process is more time-consuming - finding out how to draw the fractal, or making the Lego fit with the plan?

[legolijntje]

That looks cool.

And it is amazing you made this 100% mechanical, no mindstorms at all.

Great work! :thumbup:

[Mestari]

I was supposed to have my first post here on EB with my MOC but couldn't resist to start here by saying this is awesome! Mindstorms are great but real difficulty and challenge is in making it mechanical (and here with 1 motor only!). Congratulations :)

[Kumbbl]

For me a frontpage candidate and also a member of the new Technic Hall of Fame - Jim, what do you think? ;-)

[Philo]

Excellent!

I was curious to see the relationship between Gray code and Heighway Dragon Curve, fortunately Wikipedia provides some enlightments...

aeh5040, the string of Geneva wheels directly counts Gray code?

[TinkerBrick]

I just watched the video and i am amazed. Fantastic creation. The geneva wheel (or Maltese Cross) is brilliant. I wonder if it would be possible to "program" the device to draw other curves as well.

This goes in the same category as PG52s Auto Spirograph. Instructions would be great .

And yes. definitely a candidate for the Front Page and Hall of Fame!

[vmln8r]

This is excellent, and totally over my head. Great stuff!

[D3K]

This is amazing! Fantastic work!

The only thing I don't like is the sound of the Lego motor

[skriblez]

This is just brilliant!

[robuko]

Maths is beautiful and this is excellent engineering. Love it.

[unimog123]

That's amazing!

[Hrafn]

This is extraordinary. Bravo!

[dhc6twinotter]

I saw this in person at BrickCon, and this thing is amazing. The amount of figuring that went into this is mind-boggling.

[Zerobricks]

This is top notch mechanical engineering... Just...crazy!

[Junpei]

Absolutely mind-blowing!

TLH

[Jeroen Ottens]

Wow, combining of two great hobbies in one masterpiece

I remember programming these dragon curves in my youth, the merest possibility of the thought forming in my mind that this could be done with lego hadn't even started to materialize until I saw this video.

Very well done.

[VKTechnic]

Wasn't this at BrickCon 2013? I remember seeing it there...

Great work nonetheless!

[Rishab N]

Wow thats amazing! Nice work!

[kieran]

Very smooth, nice work

[mahjqa]

Sublime.

[Blakbird]

I remember seeing this at BrickCon and talking to you a bit about it, but I don't think I fully appreciated what it does until now. It is hard to demonstrate without a lot of space!

[Splat]

Great creation you have there

I'm always impressed by these types of mechanisms.

[captainmib]

How do you even start building something like this.

Would be very interesting to read about the thought and building process.

Awesome creation. I like mechanical stuff without dozens of pf or switches...