Random Cubes

Important: All the 3-D images in this page go to an external page because it was convenient posting it there. The links will be in large font and Green in color. You can use your mouse to rotate zoom in/out into the images. Watch in full screen for best viewing.

In this page we will see an activity done by using randomness. We have an empty space from the diagonal coordinates {-5,-5,-5} to {4,4,4}. There smaller cubes of size 1x1x1 and so you can fit 1000 cubes in the space  in total if they are stacked perfectly.

The Activity: You pick up cubes and assign a random position to it, within the space provided. I should mention that a previously assigned coordinate can be assigned again. Now we pick an increasing number of cubes in each case and see how many it takes to fill 1000 spaces. The reason you need a lot more than 1000 cubes to fill 1000 spaces is because the overlap is possible. Many cubes vanish in the process. Click to titles and it will take you to the 3D image site.

Example: Even if you pick up {1,1,1} multiple times, only one cube will be there in its position.

0. 10 Random Cubes

1. 100 Random Cubes

2.1000 Random Cubes

3. 2000 Random Cubes

4. 5000 Random Cubes

5. 10000 Random Cubes

It might appear externally that all the given space is filled when 10000 cubes are chosen for 1000 positions. But internally there still might be some spaces. It is not possible for now to represent transparent images. When it is possible, we will see things at much higher sampling.

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