Four-Dimensional Rubik's Cube Craziness

roice writes "Rubik's junkies and puzzlers will be interested in this software rendered four-dimensional analog of Rubik's Cube. With over 1.75E120 possible combinations, it's a mind bender. Free versions are available for both Windows and Linux, and they even publish their source code for download. Solving it will get your name listed in their Hall Of Fame, and there is also a running competition for the most efficient solution. To help get you started, you can check out a solution algorithm based on techniques used to solve the popular three-dimensional version."

Comments

damn it....

[deadsaijinx*]

you know how long I've been working on my three dimensional one? over a year. Perhaps I'm stupid, but that thing is impossible to solve. Anyone have any clue how long it would take a computer to solve your standard rubics cube through brute force?

Tried it a while back.

[Anonymous Coward]

Neat game. It's been around a while. I've been able to solve 7 random twists. The first thing you have to do is start with a ordered cube and see what happens when you twist it different ways. Not consistently, though. The trick is to figure out what the last move probably was, reverse it, the one before it, reverse that, and so on. After 3 random twists, you might be able to make a bad guess and recover from it. After 7, one wrong turn is a good reason for starting over. Never was able to solve a regular 3d rubiks cube puzzle though.

Anyone remember "Cubey"?

[Nova Express]

For those spared this atrocity, it was a Saturday morning cartoon featuring, I kid you not, a living Rubik's Cube. It was an idea that filled me with loathing even at that age, and I can't tell you what it was about because I always switched to something else as soon as it came on.

The 1980s certainly seemed the nadir of American animation...

Is this actualy 4D ?

[Forge]

I don't know. It looks like a more complex 3D version that's just real togh to build with plastic.

Maybe it's because I read some quack's claim that the 4th dimension was time. In which case a 4D rubics cube would solve itself over time or be onsolvable because it rescrambled while you were trying to solve.

Re:Is this actualy 4D ?

[blincoln]

Here's a Java animation that will show you a 2D projection of a 4D hypercube:

http://dogfeathers.com/java/hyprcube.html

It's really tough to wrap your head around another spatial dimension. Books like Flatland and Realware make the comparison to a 2D person's world being interrupted by one of us.

For example, if you were 2D, living on your flat plane, and a 3D person passed an orange through the plane, you would perceive it as a round shape which grew out of nothingness, got bigger and changed shape for awhile, then shrank and disappeared.

A 3D person could also see into your house, because a 2D person would just build four walls and no ceiling or floor. Similarly, a 4D creature could see through all of us and our buildings, because we only build in three dimensions.

Re:Is this actualy 4D ?

[BernardMarx]

A better way to visualize a hypercube (and to draw one on paper) is as follows:

0. Start with a point. Zero dimensions. (Draw a dot.)

1. Expand each vertex in a direction you haven't used yet. (Draw a horizontal line from the dot, and put a dot at the end of it.)

Now you have a line, one dimension.

2. Expand each vertex in a direction you haven't yet, and connect them. (Draw vertical line from each dot, and a horizontal line connecting the two new dots.)

Now you have a square, two dimensions.

3. Expand each vertex in a direction you haven't yet, and connect them. Since we have run out of actual dimensions on our sheet of paper, we will have to create virtual dimentions. Sorry if I've offended a topologist, I don't know the technical terms. (Draw one diagonal line from each of the four dots of the square, to the top and right. Connect the four new dots with another square. Most of you are probably familiar with this 2D projection of a 3D cube.)

Now you have a cube, three dimensions.

4. Expand each vertex in a direction you haven't yet, and connect them. We have to create more virtual dimensions, so this might seem a little tricky. (Imagine a cube in 3D-space, and imagine what it would look like with lines protruding from the center of the cube, through each corner. Draw these eight lines, then connect their endpoints, one square on top of the cube, one square on the bottom, then four vertical lines connecting each of the two new squares.)

If you did it correctly, you should end up with what looks like a cube, encased within a larger cube, with lines from the corners of the inner cube to the corresponding corners of the outer cube.

Re:Is this actualy 4D ?

[adamruck]

after taking calc III, Ive come up with a great way to describe 4d objects.

Example, take a room, it has 3 standard dimensions, now lets add another dimension, lets say temperature. Now we have a 4d object, we could even try and make a function to model temperature based on postion, temp = f(x,y,z);

You can even do neat things like make 3d objects out of 4d objects by taking a level surface of the 4d object. In simpler terms, take all of the points in the room that are one temperature, that will form a 3d object.

I think the easiest way to portray a 4d object is by using colour. Image taking a pair of thermal gogles and walking around a room. The only problem is that a colour approach cant be used for rubix cubes, becuase colour is already used to distinguish different sides of the cube. Perhaps to visualize a 4d rubix cube the different sides of the cube could be represented by shapes, or perhaps a numbering system. I think that taking the 4d cube and trying to flatten it into 3d looks ugly.

Re:nooo

[Jason1729]

Rubik's makes a special cube for "less intelligent puzzlers". You might want to pick up one of these.

Jason
ProfQuotes

4D analogs for mathematics behind Rubik's cube?

[kevinatilusa]

Another way of viewing the 3D Rubik's cube (for the mathematicians out there) is as a group on 6 generators, meaning that any reachable configuration could be gotten by merely repeating the same 6 operations in some order (I believe the 6 generators being rotating the two outer 3x3x1 squares 90 degrees clockwise along any of the 3 axes).

Using this group, you could do various things like find the odds that a random arrangement of stickers is actually solvable (take the size of the group divided by the number of possible arrangements). Are there computations involving this for the 4D cube on the web anywhere?

Oh my eyes!

[swordgeek]

The colours, the horrible colours!

Blue links and black test on a dark grey background. What was this guy thinking?