Below are listed various parameter values of interest for the Logistic map: x = rx(1-x). NOTE: the accuracy does not extend to all quoted digits. Keep in mind the iterative technique used. Accuracies depend on number of iterations. Superstable Periodic Orbits, period = q x 2^n Q = 1: main sequence n P r 0 1 2. 1 2 3.2360679774997897 2 4 3.4985616993277016 3 8 3.5546408627688249 4 16 3.5666673798562685 5 32 3.5692435316371103 6 64 3.5697952937499446 7 128 3.5699134654223486 8 256 3.5699387742333055 9 512 3.5699441946080649 10 1024 3.5699453554864686 11 2048 3.5699456041110785 12 4096 3.5699456573588566 13 8196 3.5699456687629000 14 16384 3.5699456712052969 15 32768 3.5699456717283835 16 65536 3.5699456718404126 17 131072 3.5699456718644058 18 262144 3.5699456718695445 Q = 3: P-3 window n P r 0 3 3.8318740552833156 1 6 3.8445687921944334 2 12 3.8483446568918460 3 24 3.8491980538753796 4 48 3.8493831104954240 5 96 3.8494228454912504 6 3*64 3.8494313602668578 7 3*128 3.8494331840868307 8 3*256 3.8494335747031799 9 3*512 3.8494336583616953 10 3*1024 3.8494336762788084 11 3*2048 3.8494336801161064 12 3*4096 3.8494336809379381 13 3*8192 3.8494336845490018 Q = 5: P-5 window (P-5 window that appears at lowest r value) n P r 0 5 3.7389149129706851 1 10 3.7418479173333612 2 20 3.7427454756951919 3 40 3.7429492045402357 4 80 3.7429934396887736 Miscellaneous Other Values Q = 7: P-7 window n P r 0 1 3.7017691535379562 1 2 3.7022833904300292 Q = 9: P-9 window n P r 0 1 3.7612551947070791 Q = 11: P-11 window n P r 0 1 3.8156748909415348 Q = 13: P-13 window n P r 0 1 3.9293579687279125 Q = 14: P-14 window n P r 0 1 3.6418242738410953 Q = 15; P-15 window n P r 0 1 3.7197112231235252 Q = 17: P-17 window n P r 0 1 3.7771219530370406 Q = 18: P-18 window n P r 0 1 3.7999441485317167 Band-Merging Criteria for 2^n bands -> 2^(n-1) bands f^p (xc) = f^q(xc), where p = Q * 3 x 2 ^ (n-1) q = Q * 2 ^ (n+1) Main sequence (Q = 1) n B r 0 1 4. 1 2 3.6785735104283219 2 4 3.5925721841069791 3 8 3.5748049387592080 4 16 3.5709859403416147 5 32 3.5701684724963751 6 64 3.5699933885591335 7 128 3.5699558913252210 8 256 3.5699478605646551 9 512 3.5699461406221058 10 1024 3.5699457722630878 11 2048 3.5699456933718672 12 4096 3.5699456764757835 13 8196 3.5699456728571457 14 16384 3.5699456720821656 P-3 window band merging (Q = 3) n B r 0 3 -> 1 1 6 -> 3 3.8511283737984412 2 12 -> 6 3.8497844467985538 3 24 -> 12 3.8495087316163259 4 48 -> 24 3.8494497396656309 5 96 -> 48 3.8494371200092967 6 3.8494344176320823 7 3.8494338388902993 8 3.8494337149424549 9 3.8494336883966707 P-5 window band merging (Q = 5) n B r 0 5 -> 1 1 10 -> 5 3.7434143352891969 2 20 -> 10 3.7430893687238083 3 40 -> 20 3.7430234795168147 4 80 -> 40 3.7430093707030432 5 160 -> 80 3.7430063531993829 6 320 -> 160 3.7430057070299307 Miscellaneous Other Values P-7 window band merging (Q = 7) n B r 0 1 1 14 -> 7 3.7025620698018953 P-9 window band merging (Q = 9) n B r 0 1 1 18 -> 9 3.7613425267224807 P-11 window band merging (Q = 11) n B r 0 1 1 22 -> 11 3.8156988548115658