Weekly Challenge Group

I think that all the challenges are interesting and they would be even more so if we did a "post-process" of what was achieved by different colleagues, drawing some useful conclusion, such as a construction method, a solution strategy, a way of think, etc. This depends a lot on the difficulties and possibilities offered by each challenge, but it always leaves something to learn and teach!

For example: did we learn anything from the cool dovetail challenge? Could a young designer looking at the challenge learn it?

I understand that this vision is not necessarily that of the creator and other participants in the group and if it's just for fun, that's fine too.

Very cool. I tried this years ago. Catia was not able to save the complete file of the level 4 Menger's sponge, but was fun anyway :)

I came up the the idea to make a screenshot of the Level 4, even if I can't save ;-)

Which software did you use? There are big differences as I could see with my model in Catia...

Working the old way... my SolidWorks 2017 reached level 5 (on an "all in one" pc with integrated video card... a real crap).

Elemental Cube 1x1x1

N1: 3x3x3 (27-7 = 20 cubes)

N2: 9x9x9 (20 fractals 1 * 20 cubes/fractal = 400 cubes)

N3: 27x27x27 (20 fractals 2 * 400 cubes/fractal = 8.000 cubes)

N4: 81x81x81 (20 fractals 3 * 8.000 cubes/fractal = 160.000 cubes)

N5: 243x243x243 (20 fractals 4 * 160.000 = 640.000 cubes)

I leave the level 5 assembly to be opened in "Large design review" mode:

Menger Sponge level 5 | 3D CAD Model Library | GrabCAD

I managed to complete the Menger Sponge level 4 in Onshape. Solidworks failed....!

https://grabcad.com/library/menger-sponge-level-4-1

I went with the Pyramid fractals. My PC packed upto level 4. Base unit was 10x10mm.

My method was to make a single unit, pattern/mate them in assembly and save the higher level are part files. This way it was easier to create higher level although my PC gave up after 4. :D I might try the Menger Sponge the same way to check how good or bad my PC is.

Highest Level my PC could generate before SW crashed why trying to save. (625 Units- weak PC)

Oh, you are using a square base. I have made a pyramid model using a triangular base. Can go up to level 5 without issues. After this, it is s l o w and annoying :-)

Sierpinski Pyramid Level 1-5

https://grabcad.com/library/sierpinski-pyramid-level-1-5-1

Now that you said, I went a bit overkill and went to Level 6 with equilateral tetrahedron as the unit.

Here are the file sizes for comparison. My weak PC managed it pretty well. :D

I like these open Sierpinsky Pyramids better because they look like real objects.

https://grabcad.com/library/open-sierpinski-pyramids-level-1-5-1

I managed to create the first two levels of the pentagons:

Grabcad model

Pentagon Ball - Level 1

This fractal design in three dimensions is really pretty. I believe that it is called a Sierpinsky Pentagon. Level 2 can be found here: https://grabcad.com/library/pentagon-ball-level-2-1

Grabcad model

Pentagon Ball - Level 2

This fractal design in three dimensions is really pretty. I believe that it is called a Sierpinsky Pentagon. Level 1 can be found here: https://grabcad.com/library/pentagon-ball-level-1-1

Hello colleagues!

I don't know the formal definition of the Sierpinsky pentagon. From what I see in the proposed solutions... does it imply a superposition (interference) of the generating geometry?

Hello Capricornio,

I don't think that there is a formal definition. The planar case is pretty self-explanatory, but you can expand this into 3-dimensions in a couple of ways, one of which results in the geometry shown above.

You basically substitute all the 'pentagonal balls' of the previous generation with the pentagon balls of the next level, each comprised of 5x as many bodies.

The big issue here is that the bodies self-intersect and ordinary boolean operations will result in invalid geometry. Therefore I had to work with surfaces and trim them individually, in order to eventually come up with one solid body as end result. But Level 3 is giving me headaches...!

ADDENDUM 14th MAY

I have discovered that the base model for this fractal is an dodecahedron. You start with a base model, a solid dodecahedron, this is level 0. Then you scale down a copy so that it fits exactly within the perimeters of the base model and can be stacked so that it completely occupies the same volume as the base model. This new array of scaled-down bodies becomes level 1. And then you repeat ad infinitum :-)

I understand Steen, I'll explore the possibilities a bit then!

I think I got to level 7. Each level took 2 arrays and I had 14 arrays total. Not really sure if that's how it's counted. But at 9 GB of memory used it was getting pretty slow so I quit. Very interesting.

Reached a new level :-)

https://grabcad.com/library/pentagon-ball-level-3-1

And generated three levels of a Sierpinski Icosahedron:

https://grabcad.com/library/sierpinski-icosahedron-level-1-2-3-1

How about a truncated icosahedron, level 1:

https://grabcad.com/library/fractal-ball-level-1-1

Have progressed to Level 2 & 3 of the truncated icosahedron:

https://grabcad.com/library/fractal-ball-alien-landscapes-1

Hello colleagues!

The pentagonal option generated a bit of frustration for me, not because it is difficult to draw, but because it implied a truncation of the dodecahedron that I considered as a generating body to "reproduce in a fractal way".

For this reason, I searched as an alternative for a fractal reproduction that starts from a dodecahedron and generates new dodecahedrons without any truncation. This is "my design intent" and I do not know what Sierpinsky's design intent was for the 3D case.

With this form of fractal growth, level 3 would be as follows (always externally inscribed in a dodecahedron):

Sierpinsky dodecahedron fractal level 3 | 3D CAD Model Library | GrabCAD

With a better generation method, consisting of replicating the previous level with a pattern driven by 3D sketches, I got to level 4 where display issues become important (on the pc I work on):

Sierpinsky dodecahedron fractal level 4 | 3D CAD Model Library | GrabCAD

Create fractals with patterns driven by 3D sketches | GrabCAD Tutorials

Okay, we are on the same page , but we go about it differently. We both fill a dodecahedron with smaller dodecahedrons, but stack them differently; mine overlap whereas yours just touch. That is, as far as I can tell, the only difference, but the end results look very different.

Yeah! There are no really deep differences. In fact, if we made a macro to automatically insert the original dodecahedron (as a kind of specialized 3D pattern) the only thing that would change would be the value assigned to the spacing parameter. However, the result of massively applying a certain rule can be surprising. We keep learning!

I would have liked to copy it 20 more times, but for lack of comfort working with the file I stop here (I will perhaps try again with my work PC...)

Fun challenge