Target: 1.618033990000·Depth: 21
Path · L = smaller · R = larger
RLRLRLRLRLRLRLRLRLRL·
Continued fraction · run-length encoding of the path
[1; 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
= 1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1)))))))))))))))))))
Best rational approximations · the convergents along the walk
| step | fraction | decimal | error | side |
|---|---|---|---|---|
| 1 | 1/1 | 1.0000000000 | 6.18e-1 | R |
| 2 | 2/1 | 2.0000000000 | 3.82e-1 | L |
| 3 | 3/2 | 1.5000000000 | 1.18e-1 | R |
| 4 | 5/3 | 1.6666666667 | 4.86e-2 | L |
| 5 | 8/5 | 1.6000000000 | 1.80e-2 | R |
| 6 | 13/8 | 1.6250000000 | 6.97e-3 | L |
| 7 | 21/13 | 1.6153846154 | 2.65e-3 | R |
| 8 | 34/21 | 1.6190476190 | 1.01e-3 | L |
| 9 | 55/34 | 1.6176470588 | 3.87e-4 | R |
| 10 | 89/55 | 1.6181818182 | 1.48e-4 | L |
| 11 | 144/89 | 1.6179775281 | 5.65e-5 | R |
| 12 | 233/144 | 1.6180555556 | 2.16e-5 | L |
| 13 | 377/233 | 1.6180257511 | 8.24e-6 | R |
| 14 | 610/377 | 1.6180371353 | 3.15e-6 | L |
| 15 | 987/610 | 1.6180327869 | 1.20e-6 | R |
| 16 | 1597/987 | 1.6180344478 | 4.58e-7 | L |
| 17 | 2584/1597 | 1.6180338134 | 1.77e-7 | R |
| 18 | 4181/2584 | 1.6180340557 | 6.57e-8 | L |
| 19 | 6765/4181 | 1.6180339632 | 2.68e-8 | R |
| 20 | 10946/6765 | 1.6180339985 | 8.52e-9 | L |
| 21 | 17711/10946 | 1.6180339850 | 4.98e-9 | · |