is there any way that someone could create a computer program to mimic 4d legos? they could create things and then show the creation from different perspectives. . ..
I was thinking about that before in fact. Have internally a 4-dimension array of boolean values, each one having 0 = not occupied, 1 = occupied.
Let the program fill this array with values calculated from a net (this is a data type I "invented" after thinking hard about how to represent shapes higher than 2 dimensions).
Once the array is filled, pick 4 directions and an origin. (To draw 3D objects, you need 3 axes which are at 3 different angles. To draw 4D you therefore need 4 different angles.) The program will then fill any occupied item in the array, after calculating what space on the screen it uses, in black, leaving empty spaces as they were. That should give you a basic representation. To see it clearer, you could have the program draw in wireframes rather than block filling areas.
As for 4D lego, I would say that it would be rather similar to our existing ones, just extruded to 1 or 2 studs in tridth/trength (I usually use tridth). This is because the lego pieces could be rotated around so they wouldn't need any "abnormal" pieces. However, there is one thing that comes to mind in Technic - there would be many different types of Technic pieces due to the fact that there are 3 possible different orientations of axial pieces; cubindical, duocylindrical and spherindrical.
Also, in the 3rd dimension we have 3 main types of gear which are - under my names - parallel, angular and worm. Parallel is where the lines that go through the centres of the gears are parallel, used to convey rotational energy across a plane, or to change the speed and force of said energy. Angular gears are where the gears are not parallel but the gears' centre-lines lie on the same plane, used to change the direction of energy. Worm gears is where the lines are not parallel nor do they lie in the same plane. These have an interesting property which is that the force is magnified greatly - in my lego set by 24 - and speed is reduced by the same multiple.
In the 4th dimension things get complicated. With cubindrically and spherindrically orientated gears we will have 4 types of gear. We still have parallel, angular and worm, but we also have realmar. Parallel and angular remain the same, while the worm's definition changes to being not in the same realm as well as not in the same plane. The realmar gear is a gear where the lines from the centres of the gears are in the same realm but not the same plane. As yet I have no idea whether the realmar gear would behave like an angular or worm gear.
With duocyndrically orientated gears we only have one, like in the second dimension, because the shape of duocylinder leaves only 2 dimensions free. This also means that duocyndrically orientated gears would be large in terms of tetra-volume and would be more costly. The type of gear we have here is one we do not encounter in the 2nd or 3rd dimensions. I will call it a free gear, since like an angular gear it can not only go around the outside of another free gear and rotate around the plane perpendicular to any line constructed between the centres of the two gears, but it can also rotate around the other remaining plane over which rotation is possible. This means that you can use two free gears and two duocyndrically orientated rods to change to any angle possible in tetraspace, whereas in realmspace you may need to use either three angular gears or two worm gears to achieve said effect. The former uses up more space and the latter has a side-effect of dramatically losing speed and gaining force.
Phew, that was a long post.
by PWrong » Mon May 31, 2004 9:51 am 
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