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Rubiks Cube

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Here is a simple model for a [http://en.wikipedia.org/wiki/Rubik%27s_cube Rubik's Cube].
 
Here is a simple model for a [http://en.wikipedia.org/wiki/Rubik%27s_cube Rubik's Cube].
   
The basic idea is that you only need to keep track of the corners and edges. Each corner has three faces. Each edge has two faces. Keeping track of a face means telling where it was before any moves were made and where it is in the current state.
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My hope is to get people to see a rubik's cube as something other than "a problem to solve." It's a toy!
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My two ideas are to get people to play with Haskel code _about_ the cube and (a separate idea, maybe to be explored in this model later) to make cubes with five colors, each edge and corner having the same coloring as each other. These markings will implicitly encourage people to focus on the interesting questions of how and when corners rotate and edges flip
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Before I started writing this, I spent months and months carying one, and sometimes several cubes around with me. I loved watching and thinking about how the different edges and corners would travel around the cube in relationship to each other.
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The basic idea of this model (below) is that you only need to keep track of the corners and edges. Each corner has three faces. Each edge has two faces. Keeping track of a face means telling where it was before any moves were made and where it is in the current state.
   
 
Choose, as a convention, the ordering, right, up, front. (Math/Physics folk: this is in anology to the "right hand rule" convention which assigns an ordering to the "x y and z" axes and determines that z will be "out of" rather than "into" the plane)
 
Choose, as a convention, the ordering, right, up, front. (Math/Physics folk: this is in anology to the "right hand rule" convention which assigns an ordering to the "x y and z" axes and determines that z will be "out of" rather than "into" the plane)

Revision as of 01:23, 16 November 2006

Here is a simple model for a Rubik's Cube.

My hope is to get people to see a rubik's cube as something other than "a problem to solve." It's a toy!

My two ideas are to get people to play with Haskel code _about_ the cube and (a separate idea, maybe to be explored in this model later) to make cubes with five colors, each edge and corner having the same coloring as each other. These markings will implicitly encourage people to focus on the interesting questions of how and when corners rotate and edges flip

Before I started writing this, I spent months and months carying one, and sometimes several cubes around with me. I loved watching and thinking about how the different edges and corners would travel around the cube in relationship to each other.

The basic idea of this model (below) is that you only need to keep track of the corners and edges. Each corner has three faces. Each edge has two faces. Keeping track of a face means telling where it was before any moves were made and where it is in the current state.

Choose, as a convention, the ordering, right, up, front. (Math/Physics folk: this is in anology to the "right hand rule" convention which assigns an ordering to the "x y and z" axes and determines that z will be "out of" rather than "into" the plane)

For example, the lower left front corner would be represented as (Left Left) (Down Down) (Front Front) before any moves are made Then, after a rotation about the Front face, the same corner, now in the right down front position would be represented as (Left Down) (Down Right) (Front Front).

#!/usr/bin/runhugs
module Main (main) where
main                    :: IO ()
main =  do putStr "Not your ordinary language"
 
data Cube = Edges Corners
 
type Edges = [Edge]
-- or Edges = Edge Edge Edge Edge Edge Edge Edge Edge Edge Edge Edge Edge
 
type Corners = [Corner]
 
data Edge = Face Face
 
data Corner = Face Face Face
 
data Face = Was Is
 
data Was = R|L|U|D|F|B
data Is =  R|L|U|D|F|B