# Symmetry Families

Rules are grouped by two transformations: left-right reflection and black-white complementation. The canonical rule is the lowest rule number in the generated family.

The 256 rules collapse into 88 local symmetry families under those transformations.

## Highest Scoring Families

| Canonical | Size | Rules | Best Rule | Best Score | Classes |
| ---: | ---: | --- | ---: | ---: | --- |
| 30 | 4 | 30 86 135 149 | 30 | 0.780 | complex |
| 134 | 4 | 134 148 158 214 | 214 | 0.717 | geometric, quiet |
| 130 | 4 | 130 144 190 246 | 190 | 0.646 | geometric, quiet |
| 152 | 4 | 152 188 194 230 | 188 | 0.634 | geometric, quiet |
| 110 | 4 | 110 124 137 193 | 137 | 0.598 | geometric |
| 106 | 4 | 106 120 169 225 | 169 | 0.576 | geometric, quiet |
| 62 | 4 | 62 118 131 145 | 62 | 0.573 | geometric |
| 150 | 1 | 150 | 150 | 0.562 | geometric |
| 90 | 2 | 90 165 | 165 | 0.561 | geometric |
| 42 | 4 | 42 112 171 241 | 241 | 0.554 | geometric, quiet |
| 46 | 4 | 46 116 139 209 | 209 | 0.554 | geometric, quiet |
| 22 | 2 | 22 151 | 151 | 0.552 | geometric |
| 26 | 4 | 26 82 167 181 | 181 | 0.542 | geometric |
| 122 | 2 | 122 161 | 161 | 0.535 | geometric, short oscillator |
| 126 | 2 | 126 129 | 129 | 0.535 | geometric |
| 34 | 4 | 34 48 187 243 | 187 | 0.530 | geometric, quiet |
| 56 | 4 | 56 98 185 227 | 185 | 0.529 | geometric, quiet |
| 18 | 2 | 18 183 | 183 | 0.525 | geometric |
| 54 | 2 | 54 147 | 54 | 0.524 | geometric, short oscillator |
| 73 | 2 | 73 109 | 73 | 0.519 | complex, geometric |
| 146 | 2 | 146 182 | 182 | 0.515 | geometric |
| 45 | 4 | 45 75 89 101 | 101 | 0.512 | complex |
| 105 | 1 | 105 | 105 | 0.490 | geometric |
| 77 | 1 | 77 | 77 | 0.481 | short oscillator |