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Hypercubes, 3Dprint and Zoetropes

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The first hypercubes we printed are a collection of 12 objects that represent 12 steps of a hypercube's full rotation around an arbitrary 4dimensional axis. The rotation was computed by Ken Perlin, who visited us at the A.R.T. Lab.

I even included little binary indicators that should allow to distinguish and sort the sculptures into the right order (see the little knobs on the bottom squares).

The print turned out to be too fragile, and some of the too thin connections broke. Important 3D-print lesson on the way: we learned that thin columns that are printed vertically are not very strong.

Also, by having a hypercube rotate the whole 360 degrees, you ultimately end up with 4 similar quarter-circle roations. Every third sculpture looks exactly the same, only rotated by 90 degrees. Not very exciting, especially since it is already very hard to make sense of what is going on with only 12 frames.

zoetrope Next we decided on printing the whole zoetrope as one object, by printing all 12 sculptures placed and attached to a flat ring. This ensures the precise positioning of all the sculptures. Small discrepancies in the placement of the objects might look like hickups in the actual animation, once rotating and seen under strobe light.

Also, instead of rotating 360 degrees, the hypercubes tumbles on the floor by only rotating 90 degrees before returning to its exact starting position. Additionally it also rotates around those 2 dimensions that are not involved in the tumbling around the circular track.

Ken made a static animation test, he rotated the platform exactly 12 parts of a circle and took pictures of it.
I built a simple and fast zoetrope mechanism, that allowed to hand-rotate the platform while the rotation would activate strobe light coming from a set of 6 super-bright LEDs.

Because of the lack of a immediately-available proper motor, we decided on hand-spinning. So a chip-activated flashing of light at a exact frequency was out of question. The hand-spinning mechanism would have to be directly linked to the flashing of the lights.

I fiddled around with it a bit, before deciding on the solution that seems most friction-less.

The bottom of the rotating platform has 12 metallic tape connections, they look like the spines of a bicycle wheel. Underneath the platform two conductive flexible springs are responsible for making a connection every time both springs touch one of the 12 metallic tape connections. This then makes the LEDs flash and our eyes perceive the object (while otherwise being in pitch black darkness).

And it all actually worked!

Also, have a look at Ken's blog posts: Another dimension and Going in circles

2010/09/05 04:20

Prototyping rotating hypercubes

Ken Perlin is visiting our lab, and he shares my interest into the fourth dimension. Which will lead to the construction of a zoetrope that will show a rotation of a 4-dimensional hypercube as a 3-dimensional 3d-printed structure.

2010/08/08 06:10

-disciplinary

I attended the conference C:ADM2010 - “Cybernetics: Art, Design, Mathematics — A Meta-Disciplinary Conversation”, July 29th - Aug 2nd in Troy, New York State. It was held at Rensselaer Polytechnic's beautiful new Experimental Media & Performing Arts Center EMPAC.

The conference title gives away that there was a lot of discussion about cross-over processes between different disciplines. Multi / Inter / Trans / Meta are the keywords. I've used these terms before, but was never really aware of their specific meaning. So, learning about the differences between all those * * * * * -disciplinarities was quite enlightening.

Here is a rough explanation from my notes

  • Multidisciplinary: several disciplines come together to work on a common subject, yet every discipline remains within their own language.
  • Interdisciplinary: several disciplines come together to work on a common subject and are able to understand and share each other's language.
  • Transdisciplinary: several disciplines come together to work on a common subject and develop a new language at the interception of their disciplines.

Here are descriptions off wikipedia

  • Multidisciplinarity is a non-integrative mixture of disciplines in that each discipline retains its methodologies and assumptions without change or development from other disciplines within the multidisciplinary relationship. [wiki]
  • Interdisciplinarity involves researchers, students, and teachers in the goals of connecting and integrating several academic schools of thought, professions, or technologies – along with their specific perspectives – in the pursuit of a common task. [wiki]
  • Transdisciplinarity has a particular emphasis on engagement, investigation, and participation in addressing present-day issues and problems in a manner that explicitly destabilizes disciplinary boundaries while respecting disciplinary expertise. [wiki]
2010/08/07 23:05

Voltage regulation and Virtual Ground in Pulse

With some help from Laurent Mignonneau i figured out how i could power my Pulse Circuit with only one power source (12 Volt), instead of three (12 Volt, 5 Volt, 10 Volt). The right capacitors keep the 7805 Voltage Regulator from heating up. And the virtual ground of 2.5 Volt at the two op-amps makes the split supply circuit (+5 and -5 Volt) unnecessary.

More on those two synchronizing oscillators

The graph on the left shows the cycle time of the oscillators A and B plotted against the resistance of the connection wire. Both measurements are displayed logarithmically.

At some point the measurements for oscillator B double, as the pulses of oscillator B group up into smaller and smaller units, that receive their own cycle time measurements (orange).

The cycle time for the grouped together pulses go conform with the measurements for oscillator A.

Interesting are the lines the measurements form on the graph. A fragmented curve that any mathematicians would immediately recognize probably.