| 2. (iii) Depending on where in the pixels its corners lie, an equilateral triangle with base
length 4 pixels may or may not have enclose empty pixels. |
| But certainly, an equilateral triangle with base length 2 pixels encloses no empty pixels. |
| Supposing P1 lies in the largest removed triangle, in part (ii) we have seen
that P2 lies in one of the three triangles of base length 512/2 = 256. |
| Continuing, we find |
| P3 lies in a triangle of base length 128 |
| P4 lies in a triangle of base length 64 |
| P5 lies in a triangle of base length 32 |
| P6 lies in a triangle of base length 16 |
| P7 lies in a triangle of base length 8 |
| P8 lies in a triangle of base length 4 |
|
| Consequently, P9, P10, ... lie in triangles consisting only of pixels occupied
by points of the gasket. |
| That is, on the computer monitor P9, P10, ... are indistinguishable from points of the gasket. |
|