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 Post subject: Deeper Madness by OSKAR
PostPosted: Sat Apr 13, 2013 6:16 am 
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Hi Twisty Puzzles fans,

Deeper Madness is a deeper-cut version of More Madness. It has a "deeper-than-deep-origin" mechanism, like Dave Pitcher's award-winning Rotoprism 2. Deeper Madness is a face-turning puzzle with six screws under the six turning faces. Starting from a screw, the associated visible cut at the surface is more than 90 degrees away.

Deeper Madness also answers Dave Pitcher's question whether a puzzle with a deeper-than-origin-cut mechanism can be solid. This puzzle shows that it can. Notice that there is still a controversy about what constitutes a deeper-than-origin-cut mechanism.

Watch the YouTube video.
Buy the puzzle at my Shapeways Shop.
Read more at the Shapeways Forum.
Check out the photos below.

Enjoy!

Oskar
Attachment:
Deeper-Madness---view-1.jpg
Deeper-Madness---view-1.jpg [ 39.91 KiB | Viewed 2009 times ]

Attachment:
Deeper-Madness---view-2.jpg
Deeper-Madness---view-2.jpg [ 34.82 KiB | Viewed 2009 times ]

Attachment:
Deeper-Madness---view-3.jpg
Deeper-Madness---view-3.jpg [ 165.11 KiB | Viewed 2009 times ]

Attachment:
Deeper-Madness---view-4.jpg
Deeper-Madness---view-4.jpg [ 48.41 KiB | Viewed 2009 times ]

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 Post subject: Re: Deeper Madness by OSKAR
PostPosted: Sat Apr 13, 2013 7:25 am 
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I'm beginning to wonder whether the names of your puzzles are supposed to reflect their complexity, or your deteriorating state of mind in coming up with such concepts: Is this a coded cry for psychiatric help? :lol:

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 Post subject: Re: Deeper Madness by OSKAR
PostPosted: Sat Apr 13, 2013 7:43 am 
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If so.. would it be bad to say "please don't get any!"? ;)

LOVE this one Oskar.. the things you come up with.. amazing!


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 Post subject: Re: Deeper Madness by OSKAR
PostPosted: Sun Apr 14, 2013 2:00 am 
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I think I already commented like this but I think I have to do it again in this case:
Now I have to write a description for this? Curse on you for challenging me like this.


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 Post subject: Re: Deeper Madness by OSKAR
PostPosted: Mon Apr 15, 2013 12:34 am 
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Amazing, Oskar.

Andreas Nortmann wrote:
Now I have to write a description for this? Curse on you for challenging me like this.

Lol. One of our goals in life as designers is to keep you on your toes, Andreas.

-Eitan

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 Post subject: Re: Deeper Madness by OSKAR
PostPosted: Thu Apr 18, 2013 2:10 am 
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The thing I'm hazy on is whether the apparent slices in this puzzle which are blocked are blocked by the core being at a wrong angle or by surface pieces at a lower hidden layer blocking things. It's easy to see how this can happen if you consider the case of the antitrivial puzzle, the one which is so deep cut that it looks like it's just trivial tips. That one would allow all kinds of crazy moves, with all kinds of blocking of moves allowed, almost none of which you could see or ascertain from the outside.

It would be fun to make something like the antitrivial puzzle which just had the tips and a floating core, but I don't see how one could make that work.


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 Post subject: Re: Deeper Madness by OSKAR
PostPosted: Thu Apr 18, 2013 3:03 am 
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Bram wrote:
The thing I'm hazy on is whether the apparent slices in this puzzle which are blocked are blocked by the core being at a wrong angle or by surface pieces at a lower hidden layer blocking things.
Things are blocked as there is no core axis aligning with the external cut, which manifests itself by pieces at a lower layer not enabling the move. Some of those lower-layer pieces may extend to the surface. It would be useful that a TP scientist would dissect this puzzle and analyze it.

Oskar

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 Post subject: Re: Deeper Madness by OSKAR
PostPosted: Thu Apr 18, 2013 8:01 am 
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Oskar wrote:
It would be useful that a TP scientist would dissect this puzzle and analyze it.
I don't know that I'm a scientist, but I have finally come to a better understanding of the geometry of this puzzle, so I'll give my analysis here.

Previously, I had been looking at these puzzles as an origin point, a set of axes, and a slice pattern on the surface of the outer geometric shape. While that is a good way of examining the puzzles, it is incomplete. A better way to view the geometry is to actually slice the form, and examine the resulting pieces as they align with the origin point and the axes. I'll demonstrate with a very easy example, the Rubik's Cube:

First, we have a sliced cube. The orbiting cubies are white, and the axle cubies are colored yellow. These are the cubies that can be screwed to the core in a mechanical implementation of the puzzle. They also represent the axes of the puzzle, which for the purposes of defining the geometry as shallow-cut, origin-cut, or deeper-than-origin-cut, remain stationary in space. The core itself is red. Here is an image of the outside of the puzzle. Note that the axle parts are visible:
Attachment:
cube geometry example 1.jpg
cube geometry example 1.jpg [ 63.07 KiB | Viewed 1445 times ]
Next, I've made the turning layer see-through:
Attachment:
cube geometry example 2.jpg
cube geometry example 2.jpg [ 69.5 KiB | Viewed 1445 times ]
Next, I've removed the pieces of the turning layer (excepting the axle):
Attachment:
cube geometry example 3.jpg
cube geometry example 3.jpg [ 59.35 KiB | Viewed 1445 times ]
Then I've removed the axle so that the core is visible:
Attachment:
cube geometry example 4.jpg
cube geometry example 4.jpg [ 59.29 KiB | Viewed 1445 times ]
Finally, I've removed the remaining orbiting parts to reveal only the axles (minus the one from the turning layer) and the core:
Attachment:
cube geometry example 5.jpg
cube geometry example 5.jpg [ 48.49 KiB | Viewed 1445 times ]
One can readily see that this is a shallow-cut geometry since turning a deep slice would also turn the origin and five other axes, relocating them in space.

Now let's go through the same exercise with a jumbling puzzle, More Madness. It's more complex, but the same principles still apply. Planar slices are used, and they are shallower than the origin. First is the complete puzzle (note that the axle parts are not yet visible):
Attachment:
more madness 1.jpg
more madness 1.jpg [ 58.08 KiB | Viewed 1445 times ]
Next the turning slice is made clear:
Attachment:
more madness 2.jpg
more madness 2.jpg [ 66.58 KiB | Viewed 1445 times ]
Next the turning slice is removed:
Attachment:
more madness 3.jpg
more madness 3.jpg [ 54.16 KiB | Viewed 1445 times ]
Then the turning axle part is removed, revealing the core:
Attachment:
more madness 4.jpg
more madness 4.jpg [ 53.11 KiB | Viewed 1445 times ]
Finally, the remaining orbiting parts are removed:
Attachment:
more madness 5.jpg
more madness 5.jpg [ 36.76 KiB | Viewed 1445 times ]
With these images, it can be seen that More Madness is indeed a face-turning shallow-cut puzzle.

Now we get to the heart of the matter, Deeper Madness. Here is the same sequence of images, starting with the complete puzzle:
Attachment:
deeper madness 1.jpg
deeper madness 1.jpg [ 57.82 KiB | Viewed 1445 times ]
Next, the turning slice is made clear. Note that in this case, the turning slice is actually an edge slice:
Attachment:
deeper madness 2.jpg
deeper madness 2.jpg [ 65.05 KiB | Viewed 1445 times ]
Now the orbiting parts of the turning slice are removed:
Attachment:
deeper madness 3.jpg
deeper madness 3.jpg [ 55.66 KiB | Viewed 1445 times ]
Then the turning axle part is removed, revealing the core:
Attachment:
deeper madness 4.jpg
deeper madness 4.jpg [ 55.89 KiB | Viewed 1445 times ]
Finally the remaiing orbiting parts are removed:
Attachment:
deeper madness 5.jpg
deeper madness 5.jpg [ 39.63 KiB | Viewed 1445 times ]
With this sequence of images it can be seen that in order for the core and axis system to remain stationary in space, a face of the puzzle geometry is "held", and the edge is turned. This allows only the edge axle and axis to rotate, leaving the rest of the parts unaffected. Despite the fact that the cutting planes are parallel to the faces, and are deeper than the origin relative to the faces, this geometry should be viewed as shallow-cut. My guess is that the physical puzzle might be easier to understand and manipulate if played as an edge-turning shallow-cut puzzle.

Note that the shallow-cut nature of the geometry of the puzzle does not preclude the mechanism from being deeper-than-origin cut. If the axle parts of the puzzle as designed by Oskar are located underneath the faces of the puzzle, then this would be a deeper-than-origin mechanism. I suspect this might also provide an explanation for why axes can sometimes become blocked by interior pieces without any visible blocking on the exterior. I also suspect that a new version of the puzzle based on a shallow-cut edge-turning mechanism would avoid this type of invisible blocking. If true, the result would be a different puzzle than the current version, although it would look exactly the same from the outside.

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 Post subject: Re: Deeper Madness by OSKAR
PostPosted: Thu Apr 18, 2013 12:44 pm 
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Dave,

Great sketches!
David Pitcher wrote:
Despite the fact that the cutting planes are parallel to the faces, and are deeper than the origin relative to the faces, this geometry should be viewed as shallow-cut. My guess is that the physical puzzle might be easier to understand and manipulate if played as an edge-turning shallow-cut puzzle.
Are you contradicting yourself now? If one plays Deeper Madness as a shallow-cut puzzle, then one would get confused by some blocked moves, which are only understood by playing the puzzle using deeper-than-origin moves and keeping the orientation of the turning axes fixed. That was the argument that you made earlier in favor of playing Rotoprism 2 using only deeper-than-origin moves. I am confused.

Oskar

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 Post subject: Re: Deeper Madness by OSKAR
PostPosted: Thu Apr 18, 2013 2:16 pm 
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Oskar wrote:
Are you contradicting yourself now? If one plays Deeper Madness as a shallow-cut puzzle, then one would get confused by some blocked moves, which are only understood by playing the puzzle using deeper-than-origin moves and keeping the orientation of the turning axes fixed.
No, I do mean that Deeper Madness should be played as a shallow-cut edge turning puzzle because this is the play mode that keeps the origin and five non-turning axes fixed in space during any one move. This is the same argument for playing RotoPrism 2 as a deeper-than-origin puzzle, since to use it as a shallow-cut puzzle turns the origin and relocates the remaining two axes. This is particularly problematic with 90 degree turns (as you know, you can get away with shallow 180 degree turns since the axes return to their original orientations).

Regarding Deeper madness, are the parts that get screwed into the core underneath the face centers, or are they located under the edges, in the same position as the yellow axle parts in my drawings?

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 Post subject: Re: Deeper Madness by OSKAR
PostPosted: Thu Apr 18, 2013 2:35 pm 
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Dave,

The screws are under the faces, and the cut is deeper-than-origin. Making deeper-than-origin turns requires one to turn the faces, which are the bulk of the puzzle. This way, the six axes are kept with a fixed orientation in space.

Oskar

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 Post subject: Re: Deeper Madness by OSKAR
PostPosted: Thu Apr 18, 2013 9:19 pm 
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Oskar wrote:
The screws are under the faces
It would be very interesting to try a version of the Deeper Madness puzzle where the axles (and axes) are located under the edges, where my analysis above indicates that they "should" be located. I wonder if this would eliminate the problem of hidden bandaging, where layers are blocked even though they don't appear to be from the outside. Any chance this could be one of your next puzzles Oskar?

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 Post subject: Re: Deeper Madness by OSKAR
PostPosted: Sat Apr 27, 2013 3:09 am 
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Here is the cut curve of Deeper Madness. It is obviously a deeper-than-origin cut.

Oskar
Attachment:
Deeper Madness - view 5.jpg
Deeper Madness - view 5.jpg [ 37.06 KiB | Viewed 1057 times ]

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