| 1 | The Hilbert Curve: | ||||||||||
| Level # | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
| # of Line Segments | 1 | 9 | 81 | 729 | 6561 | 59049 | 531441 | 4782969 | 43046721 | 387420489 | |
| Size of Line Segments | 1 | 1/3 | 1/9 | 1/27 | 1/81 | 1/243 | 1/729 | 2187 | 6561 | 19683 | |
| Describe the pattern for the number of line segments: | |||||||||||
| Describe the pattern for the size of the line segments: | |||||||||||
| 2 | Another Hilbert Curve | ||||||||||
| Level # | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
| # of Line Segments | 1 | 8 | 64 | 512 | 4096 | 32768 | 262144 | 2097152 | 16777216 | 134217728 | |
| Size of Line Segments | 1 | 1/3 | 1/9 | 1/27 | 1/81 | 1/243 | 1/729 | 2187 | 6561 | 19683 | |
| Describe the pattern for the number of line segments: | |||||||||||
| Describe the pattern for the size of the line segments: | |||||||||||
| 3 | Sierpinski's Carpet | ||||||||||
| Level # | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
| # of Squares | 1 | 8 | 64 | 512 | 4096 | 32768 | 262144 | 2097152 | 16777216 | 134217728 | |
| Length of Each Side | 1 | 1/3 | 1/9 | 1/27 | 1/81 | 1/243 | 1/729 | 2187 | 6561 | 19683 | |
| Describe the pattern for the number of squares: | |||||||||||
| Describe the pattern for the length of each side: | |||||||||||
| 4 | Sierpinski's Triangle | ||||||||||
| Level # | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
| # of Triangles | 1 | 3 | 9 | 27 | 81 | 243 | 729 | 2187 | 6561 | 19683 | |
| Length of Each Side | 1 | 1/2 | 1/4 | 1/8 | 1/16 | 1/32 | 1/64 | 1/128 | 1/256 | 1/512 | |
| Describe the pattern for the number of triangles: | |||||||||||
| Describe the pattern for the length of each side: | |||||||||||
| 5 | Koch's Snowflake | ||||||||||
| Level # | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
| # of Line Segments | 3 | 12 | 48 | 192 | 768 | 3072 | 12288 | 49152 | 196608 | 786432 | |
| Size of Line Segments | 1 | 1/3 | 1/9 | 1/27 | 1/81 | 1/243 | 1/729 | 2187 | 6561 | 19683 | |
| Describe the pattern for the number of line segments: | |||||||||||
| Describe the pattern for the size of the line segments: | |||||||||||