based on : G ALVAREZ, M ROMERA, G PASTOR and F MONTOYA: Determination of Mandelbrot Set|s Hyperbolic Component Centres. Chaos, Solitons & Fractals Vol 9 No 12 pp 1997-2005,1998 Shows centers c for periods 1-10 At the end of list is Maxima program for coputing centers. It was used for computing this list center c [symbolic sequence] internal address ======================================================= period = 1 c= 0.0 [C] 1 ----------------------- period =2 c = -1.0 [C,L] 1-2 ---------------------- period=3 c = -0.1225611668767 + 0.7448617666197*%i [C,L,L] 1-3 -0.1225611668767 - 0.7448617666197*%i [C,L,L] 1-3 -1.75487766624669 [C,L,R] --------------------------------------------------- period =4 c = 0.2822713907669 + 0.5300606175785*%i [C,R,R,L] 0.2822713907669 - 0.5300606175785*%i [C,R,R,L] -0.1565201668338 - 1.03224710892283*%i [C,L,L,R] -0.1565201668338 + 1.03224710892283*%i [C,L,L,R] -1.31070264133683 [C,L,R,L] -1.94079980652948 [C,L,R,R] ----------------------------------------- period =5 c = 0.3349323055975*%i+0.3795135880159 [C,R,R,R,L] 0.562765761453*%i-0.5043401754462 [C,L,L,L,L] 0.3795135880159-0.3349323055975*%i [C,R,R,R,L] 0.359259224758-0.6425137371385*%i [C,R,R,L,R] 0.6425137371385*%i+0.359259224758 [C,R,R,L,R] -0.562765761453*%i-0.5043401754462 [C,L,L,L,L] -0.9865809762809*%i-0.04421235770407 [C,L,L,R,L] 0.9865809762809*%i-0.04421235770406 [C,L,L,R,L] 1.1002695372927*%i-0.1980420993643 [C,L,L,R,R] -1.10026953729269*%i-0.1980420993643 [C,L,L,R,R] -0.3803209634727*%i-1.2563679300682 [C,L,R,L,R] 0.3803209634728*%i-1.25636793006826 [C,L,R,L,R] -1.62541372512275 [C,L,R,L,L] -1.86078252220592 [C,L,R,R,L] -1.9854242530536 [C,L,R,R,R] --------------------------------------------- ============================================= ================================================ period =6 c = 0.2158506508708*%i+0.3890068405698 [C,R,R,R,R,L] 0.3890068405698-0.2158506508708*%i [C,R,R,R,R,L] 0.4433256333996-0.3729624166628*%i [C,R,R,R,L,R] 0.3729624166628*%i+0.4433256333996 [C,R,R,R,L,R] 0.6847620202118*%i+0.3598927390126 [C,R,R,L,R,R] 0.604181810489*%i+0.3965345700324 [C,R,R,L,L,L] 0.3965345700324-0.604181810489*%i [C,R,R,L,L,L] 0.3598927390126-0.6847620202119*%i [C,R,R,L,R,R] 0.8605694725015*%i-0.1134186559496 [C,L,L,R,L,L] 0.6629807445769*%i-0.5968916446449 [C,L,L,L,L,R] -0.8605694725038*%i-0.1134186559483 [C,L,L,R,L,L] -0.662980744572*%i-0.5968916446433 [C,L,L,L,L,R] 1.02049736649822*%i-0.01557038602045 [C,L,L,R,L,R] 1.09778064289024*%i-0.1635982615528 [C,L,L,R,R,L] -1.09778064288989*%i-0.1635982615585 [C,L,L,R,R,L] -1.02049736649939*%i-0.0155703860209 [C,L,L,R,L,R] 0.2403324010959*%i-1.13800066642939 [C,L,R,L,R,L] -0.2403324015024*%i-1.13800066649985 [C,L,R,L,R,L] 1.11445426587145*%i-0.2175267470305 [C,L,L,R,R,R] -1.11445426586931*%i-0.2175267470267 [C,L,L,R,R,R] -0.4272688960728*%i-1.28408492564555 [C,L,R,L,R,R] 0.4272688961382*%i-1.28408492541968 [C,L,R,L,R,R] -1.47601464324719 [C,L,R,L,L,L] -1.90728008309472 [C,L,R,R,L,L] -1.77289290448378 [C,L,R,R,L,R] -1.99637612979443 [C,L,R,R,R,R] -1.96677323101826 [C,L,R,R,R,L] ----------------------------------------------- ------------------------------------------------ ----------------------------------------------- ------------------------------------------------- period = 7 c = 0.1447493713216*%i+0.3760086818468 [C,R,R,R,R,R,L] 0.3760086818468-0.1447493713216*%i [C,R,R,R,R,R,L] 0.432376192642-0.2267599044353*%i [C,R,R,R,R,L,R] 0.2267599044353*%i+0.432376192642 [C,R,R,R,R,L,R] 0.3477587008835*%i+0.4568232858233 [C,R,R,R,L,L,L] 0.4568232858233-0.3477587008835*%i [C,R,R,R,L,L,L] 0.4527744987249-0.3961701280332*%i [C,R,R,R,L,R,R] 0.5693247113031*%i+0.3865391765962 [C,R,R,L,L,R,L] 0.3961701280332*%i+0.4527744987249 [C,R,R,R,L,R,R] 0.1211927861059-0.6106116922108*%i [C,R,L,L,R,L,L] 0.6106116922108*%i+0.1211927861059 [C,R,L,L,R,L,L] 0.6682887255592*%i-0.5308278048599 [C,L,L,L,L,R,L] 0.3865391765962-0.5693247113031*%i [C,R,R,L,L,R,L] 0.6983372395833*%i+0.3524825397224 [C,R,L,L,R,R,R] 0.4248784364756*%i-0.6224362950413 [C,L,L,L,L,L,L] 0.4129160247227-0.6148067601434*%i [C,R,R,L,L,L,R] 0.6148067601434*%i+0.4129160247227 [C,R,R,L,L,L,R] 0.6785686931904*%i+0.3768932403793 [C,R,R,L,R,L,L] -0.4248784364756*%i-0.6224362950413 [C,L,L,L,L,L,L] 0.3524825397224-0.6983372395833*%i [C,R,L,L,R,R,R] 0.3768932403793-0.6785686931904*%i [C,R,R,L,R,L,L] 0.01489546660369-0.8481487619084*%i [C,R,L,L,L,L,R] 0.4081043241127*%i-1.26228728143847 [C,L,R,L,R,R,L] -0.6682887255592*%i-0.5308278048599 [C,L,L,L,L,R,L] 0.8481487619084*%i+0.01489546660369 [C,R,L,L,L,L,R] 0.6810644142252*%i-0.6235324859563 [C,L,L,L,L,R,R] -0.8423646902941*%i-0.2721024614889 [C,L,L,R,L,L,R] -0.6810644142252*%i-0.6235324859563 [C,L,L,L,L,R,R] 0.8423646902941*%i-0.2721024614889 [C,L,L,R,L,L,R] 1.11626015745499*%i-0.2249159512867 [C,L,L,R,R,R,R] -1.10900651411361*%i-0.157516053476 [C,L,L,R,R,L,R] 1.11748077249496*%i-0.2072838354557 [C,L,L,R,R,R,L] -1.00360386228829*%i-0.006983568496261 [C,L,L,R,L,R,L] 1.03291477521364*%i-0.01423348192035 [C,L,L,R,L,R,R] 1.10900651411361*%i-0.157516053476 [C,L,L,R,R,L,R] -1.03291477521364*%i-0.01423348192035 [C,L,L,R,L,R,R] 0.9874609094895*%i-0.1274999735464 [C,L,L,R,L,L,L] -0.9874609094895*%i-0.1274999735464 [C,L,L,R,L,L,L] 1.00360386228829*%i-0.006983568496261 [C,L,L,R,L,R,L] 1.07142767145403*%i-0.1745782211357 [C,L,L,R,R,L,L] -1.07142767145403*%i-0.1745782211357 [C,L,L,R,R,L,L] -1.11748077249496*%i-0.2072838354557 [C,L,L,R,R,R,L] 0.3613765171186*%i-1.02819385245482 [C,L,L,L,R,L,R] -0.3613765171186*%i-1.02819385245482 [C,L,L,L,R,L,R] -1.11626015745499*%i-0.2249159512867 [C,L,L,R,R,R,R] -0.3424706478898*%i-1.25273588401204 [C,L,R,L,R,L,L] -0.1361719973047*%i-1.40844648574007 [C,L,R,L,L,L,R] -0.4381988160866*%i-1.29255806103352 [C,L,R,L,R,R,R] -1.5748891397523 [C,L,R,L,L,L,L] 0.1361719973047*%i-1.40844648574007 [C,L,R,L,L,L,R] 0.3424706478898*%i-1.25273588401204 [C,L,R,L,R,L,L] -0.4081043241127*%i-1.26228728143847 [C,L,R,L,R,R,L] 0.4381988160866*%i-1.29255806103352 [C,L,R,L,R,R,R] -1.83231520275123 [C,L,R,R,L,R,L] -1.88480357158668 [C,L,R,R,L,L,L] -1.9537058942844 [C,L,R,R,R,L,R] -1.92714770936395 [C,L,R,R,L,L,R] -0.0569195003956*%i-1.76926167027683 [C,L,R,R,L,R,R] 0.0569195003956*%i-1.76926167027683 [C,L,R,R,L,R,R] -1.67406609147479 [C,L,R,L,L,R,L] -1.99181417254912 [C,L,R,R,R,R,L] -1.97717958700626 [C,L,R,R,R,L,L] -1.99909568232702 [C,L,R,R,R,R,R] ------------------------------------------------------ ====================================================== ======================================================= ======================================================= ======================================================== period =8 c = 0.1009348768643*%i+0.3590310628366[C,R,R,R,R,R,R,L] 0.3590310628366-0.1009348768643*%i[C,R,R,R,R,R,R,L] 0.4048996651751-0.1458203637666*%i[C,R,R,R,R,R,L,R] 0.1458203637666*%i+0.4048996651751[C,R,R,R,R,R,L,R] 0.3319313877261*%i+0.4505288596136[C,R,R,R,L,L,R,L] 0.4065209922881*%i+0.4511458035917[C,R,R,R,L,R,R,R] 0.2103812005985*%i+0.4372839294972[C,R,R,R,R,L,L,L] 0.4420745300155-0.2394260402866*%i[C,R,R,R,R,L,R,R] 0.4372839294972-0.2103812005985*%i[C,R,R,R,R,L,L,L] 0.2394260402866*%i+0.4420745300155[C,R,R,R,R,L,R,R] 0.466959205647-0.351546724574*%i[C,R,R,R,L,L,L,R] 0.4617031682021-0.3901102379498*%i[C,R,R,R,L,R,L,L] 0.4505288596136-0.3319313877261*%i[C,R,R,R,L,L,R,L] 0.565397856798*%i+0.4030334586863[C,R,R,L,L,R,L,R] 0.351546724574*%i+0.466959205647[C,R,R,R,L,L,L,R] 0.4511458035917-0.4065209922881*%i[C,R,R,R,L,R,R,R] 0.3901102379498*%i+0.4617031682021[C,R,R,R,L,R,L,L] 0.5638156221403*%i+0.3248197014655[C,R,R,L,R,R,R,L] 0.3248197014655-0.5638156221403*%i[C,R,R,L,R,R,R,L] 0.6173534533988*%i-0.3591023901124[C,L,L,L,L,L,L,L] 0.1357822388398-0.6708559100947*%i[C,R,L,L,R,R,L,R] 0.6708559100947*%i+0.1357822388398[C,R,L,L,R,R,L,R] -1.11259061359309*%i-0.157781855891[C,L,L,R,R,L,R,R] 0.4161469132252-0.6073949094159*%i[C,R,R,L,L,L,L,L] 0.4030334586863-0.565397856798*%i[C,R,R,L,L,R,L,R] 0.6838314618404*%i+0.3807223698499[C,R,R,L,R,L,L,R] -0.6173534533988*%i-0.3591023901124[C,L,L,L,L,L,L,L] 0.6073949094159*%i+0.4161469132252[C,R,R,L,L,L,L,L] 0.3473586076513-0.7015597670608*%i[C,R,L,L,R,R,R,R] 0.6992157664417*%i+0.3593256578334[C,R,L,L,R,R,L,L] 0.3771492865682-0.6668787779162*%i[C,R,R,L,R,L,R,L] 0.4149787847486-0.6210078074038*%i[C,R,R,L,L,L,R,R] 0.3030408865645*%i-1.18561119304423[C,L,R,L,R,L,L,L] 0.6668787779162*%i+0.3771492865682[C,R,R,L,R,L,R,L] 0.3593256578334-0.6992157664417*%i[C,R,L,L,R,R,L,L] 0.7015597670608*%i+0.3473586076513[C,R,L,L,R,R,R,R] 0.6210078074038*%i+0.4149787847486[C,R,R,L,L,L,R,R] 0.02286053325955-0.8136699182346*%i[C,R,L,L,R,L,R,L] 0.3807223698499-0.6838314618404*%i[C,R,R,L,R,L,L,R] 0.8136699182346*%i+0.02286053325955[C,R,L,L,R,L,R,L] -0.8704874213146*%i-0.2404161947377[C,L,L,R,L,L,R,L] 0.3863120832165*%i-1.0289695190244[C,L,L,L,R,L,R,R] 0.684031616476*%i-0.6061855588948[C,L,L,L,L,R,R,L] -0.684031616476*%i-0.6061855588948[C,L,L,L,L,R,R,L] 0.465349538581*%i-0.690942897652[C,L,L,L,L,L,L,R] 0.6213486892614*%i-0.5924659027468[C,L,L,L,L,R,L,L] -0.465349538581*%i-0.690942897652[C,L,L,L,L,L,L,R] -0.6969436485521*%i-0.5259710825307[C,L,L,R,L,R,L,R] 0.2653875324684*%i-0.9994423872066[C,L,L,L,R,L,R,L] -0.6213486892614*%i-0.5924659027468[C,L,L,L,L,R,L,L] 0.8646977200385*%i+0.02597052296021[C,R,L,L,L,L,R,R] 0.02597052296021-0.8646977200385*%i[C,R,L,L,L,L,R,R] 0.4339438723276*%i-1.28648120031329[C,L,R,L,R,R,R,L] 0.6969436485521*%i-0.5259710825307[C,L,L,R,L,R,L,R] -0.8451545288846*%i-0.2963503648637[C,L,L,R,L,L,R,R] 0.8451545288846*%i-0.2963503648637[C,L,L,R,L,L,R,R] -0.6847017576232*%i-0.6323841219692[C,L,L,L,L,R,R,R] 0.8704874213146*%i-0.2404161947377[C,L,L,R,L,L,R,L] 0.6847017576232*%i-0.6323841219692[C,L,L,L,L,R,R,R] -1.0296301183616*%i-0.009862436986086[C,L,L,R,L,R,R,L] 1.11259061359309*%i-0.157781855891[C,L,L,R,R,L,R,R] -1.03664566584786*%i-0.01560853322385[C,L,L,R,L,R,R,R] 0.4132250097757*%i-1.24257802818751[C,L,R,L,R,R,L,R] 1.11837588920162*%i-0.2222356541797[C,L,L,R,R,R,R,L] 1.03731324081042*%i-0.1628677070673[C,L,L,R,R,L,L,R] 4.642174475406209E-4-1.00450102292427*%i[C,R,L,R,L,R,L,R] 0.9705421368992*%i-0.07447045138003[C,L,L,R,L,L,L,L] -0.9989926446849*%i-0.02324229196116[C,L,L,R,L,R,L,L] -1.03731324081042*%i-0.1628677070673[C,L,L,R,R,L,L,R] 1.03664566584786*%i-0.01560853322385[C,L,L,R,L,R,R,R] -1.10439546107771*%i-0.1544546176436[C,L,L,R,R,L,R,L] 1.10913294441865*%i-0.2079914317766[C,L,L,R,R,R,L,L] -1.09156042918686*%i-0.1831734499823[C,L,L,R,R,L,L,L] 1.10439546107771*%i-0.1544546176436[C,L,L,R,R,L,R,L] -0.9705421368992*%i-0.07447045138003[C,L,L,R,L,L,L,L] 1.12138330310092*%i-0.2065986098698[C,L,L,R,R,R,L,R] 1.00450102292427*%i+4.642174475406209E-4[C,R,L,R,L,R,L,R] -0.2653875324684*%i-0.9994423872066[C,L,L,L,R,L,R,L] 1.0296301183616*%i-0.009862436986086[C,L,L,R,L,R,R,L] 1.09156042918686*%i-0.1831734499823[C,L,L,R,R,L,L,L] 0.9989926446849*%i-0.02324229196116[C,L,L,R,L,R,L,L] -1.10913294441865*%i-0.2079914317766[C,L,L,R,R,R,L,L] -1.12138330310092*%i-0.2065986098698[C,L,L,R,R,R,L,R] 1.11588359859402*%i-0.227331323047[C,L,L,R,R,R,R,R] -0.3863120832165*%i-1.0289695190244[C,L,L,L,R,L,R,R] -1.11837588920162*%i-0.2222356541797[C,L,L,R,R,R,R,L] -1.11588359859402*%i-0.227331323047[C,L,L,R,R,R,R,R] -0.4339438723276*%i-1.28648120031329[C,L,R,L,R,R,R,L] -0.4409374356744*%i-1.2951891635854[C,L,R,L,R,R,R,R] -0.3030408865645*%i-1.18561119304423[C,L,R,L,R,L,L,L] 2.420849683857182E-34*%i-1.38154748443206[C,L,R,L,L,L,R,L] -0.3527071237234*%i-1.28567733021373[C,L,R,L,R,L,L,R] -4.099427665488497E-24*%i-1.99977404869373[C,L,R,R,R,R,R,R] -0.1564428438762*%i-1.42345445853315[C,L,R,L,L,L,R,R] 0.4409374356744*%i-1.2951891635854[C,L,R,L,R,R,R,R] -0.4132250097757*%i-1.24257802818751[C,L,R,L,R,R,L,R] 0.418316059834*%i-1.28153310531949[C,L,R,L,R,R,L,L] -0.04172670614645*%i-1.76649514799364[C,L,R,R,L,R,R,L] -0.06390433171489*%i-1.77071320129695[C,L,R,R,L,R,R,R] -0.418316059834*%i-1.28153310531949[C,L,R,L,R,R,L,L] 0.3527071237234*%i-1.28567733021373[C,L,R,L,R,L,L,R] 0.1564428438762*%i-1.42345445853315[C,L,R,L,L,L,R,R] 0.06390433171489*%i-1.77071320129695[C,L,R,R,L,R,R,R] -0.02214573651725*%i-1.62792906520434[C,L,R,L,L,R,L,R] 0.02214573651725*%i-1.62792906520434[C,L,R,L,L,R,L,R] 1.135906995915311E-27*%i-1.71107947001315[C,L,R,L,L,R,L,L] -6.411677556504232E-26*%i-1.81000138572801[C,L,R,R,L,R,L,L] -1.254654288417935E-31*%i-1.52181723167125[C,L,R,L,L,L,L,L] 6.309434767577679E-25*%i-1.89691799467883[C,L,R,R,L,L,L,L] -7.882277993173255E-25*%i-1.91709827711342[C,L,R,R,L,L,R,L] 7.130394189871153E-24*%i-1.97219983836688[C,L,R,R,R,L,L,L] 1.202731911637393E-24*%i-1.9417820903182[C,L,R,R,R,L,R,R] -4.688300085214373E-25*%i-1.87000388082877[C,L,R,R,L,L,L,R] -3.306130142564657E-24*%i-1.96075898719743[C,L,R,R,R,L,R,L] 2.779644218302756E-25*%i-1.85173004941064[C,L,R,R,L,R,L,R] 1.475042512718511E-23*%i-1.98879327430947[C,L,R,R,R,R,L,R] -1.463534155068282E-23*%i-1.99433296671553[C,L,R,R,R,R,L,L] 0.04172670614645*%i-1.76649514799364[C,L,R,R,L,R,R,L] -1.166082845187596E-23*%i-1.98165578627604[C,L,R,R,R,L,L,R] 1.101408163271817E-23*%i-1.99796291559771[C,L,R,R,R,R,R,L] -------------------------------------------------------------------- -------------======================================================= ===================================================================== ===================================================================== ===================================================================== period = 9 c = 0.0728423778876*%i+0.3432044931556[C,R,R,R,R,R,R,R,L] 0.09855801111838*%i+0.3786081241329[C,R,R,R,R,R,R,L,R] 0.3432044931556-0.0728423778876*%i[C,R,R,R,R,R,R,R,L] 0.3786081241329-0.09855801111838*%i[C,R,R,R,R,R,R,L,R] 0.2466640335878*%i+0.4429369373918[C,R,R,R,R,L,R,R,R] 0.4064472370251-0.1349020908514*%i[C,R,R,R,R,R,L,L,L] 0.1349020908514*%i+0.4064472370251[C,R,R,R,R,R,L,L,L] 0.4129629397222-0.1528462818977*%i[C,R,R,R,R,R,L,R,R] 0.3250473129954*%i+0.4367094369404[C,R,R,R,L,L,R,R,L] 0.1528462818977*%i+0.4129629397222[C,R,R,R,R,R,L,R,R] 0.4328641194348-0.2017924057803*%i[C,R,R,R,R,L,L,R,L] 0.2017924057803*%i+0.4328641194348[C,R,R,R,R,L,L,R,L] 0.4438516030776-0.2116446567866*%i[C,R,R,R,R,L,L,L,R] 0.2116446567866*%i+0.4438516030776[C,R,R,R,R,L,L,L,R] 0.4468910033081-0.2344758287452*%i[C,R,R,R,R,L,R,L,L] 0.4429369373918-0.2466640335878*%i[C,R,R,R,R,L,R,R,R] 0.2344758287452*%i+0.4468910033081[C,R,R,R,R,L,R,L,L] 0.4577035456019-0.3295355101341*%i[C,R,R,R,L,L,R,L,R] 0.3289029472965-0.410912590893*%i[C,R,R,L,L,R,R,R,L] 0.4689707820982-0.3550906393105*%i[C,R,R,R,L,L,L,R,R] 0.4367094369404-0.3250473129954*%i[C,R,R,R,L,L,R,R,L] 0.520161401873*%i+0.3616150715133[C,R,R,L,L,R,R,L,R] 0.3472622588195*%i+0.4683191764052[C,R,R,R,L,L,L,L,L] 0.4616697123713-0.3840535738296*%i[C,R,R,R,L,R,L,R,L] 0.410912590893*%i+0.3289029472965[C,R,R,L,L,R,R,R,L] 0.3840535738296*%i+0.4616697123713[C,R,R,R,L,R,L,R,L] 0.3928539457586*%i+0.4645992214774[C,R,R,R,L,R,L,L,R] 0.6646219888599*%i+0.3636207176041[C,R,R,L,R,R,R,R,L] 0.3550906393105*%i+0.4689707820982[C,R,R,R,L,L,L,R,R] 0.6079685443396*%i+0.4191627819847[C,R,R,L,L,L,L,L,R] 0.3295355101341*%i+0.4577035456019[C,R,R,R,L,L,R,L,R] 0.4645992214774-0.3928539457586*%i[C,R,R,R,L,R,L,L,R] 0.4683191764052-0.3472622588195*%i[C,R,R,R,L,L,L,L,L] 0.410223157457*%i+0.4480920118978[C,R,R,R,L,R,R,R,R] 0.4558794895195-0.406047513722*%i[C,R,R,R,L,R,R,L,L] 0.3616150715133-0.520161401873*%i[C,R,R,L,L,R,R,L,R] 0.667190207251*%i-0.5639672957349[C,L,L,L,L,R,L,L,L] 0.4480920118978-0.410223157457*%i[C,R,R,R,L,R,R,R,R] 0.406047513722*%i+0.4558794895195[C,R,R,R,L,R,R,L,L] 0.2628305450022-0.6122595737352*%i[C,R,L,L,R,R,R,L,R] 0.5681273458735*%i+0.4075032522891[C,R,R,L,L,R,L,R,R] 0.4191627819847-0.6079685443396*%i[C,R,R,L,L,L,L,L,R] 0.3597833828653-0.7016533637958*%i[C,R,L,L,R,R,L,L,R] 0.4075032522891-0.5681273458735*%i[C,R,R,L,L,R,L,R,R] 0.132543247674-0.6862355387979*%i[C,R,L,L,R,L,L,R,R] 0.6601857031416*%i+0.1560476300436[C,R,L,L,R,R,L,R,L] 0.4013069326432-0.5586988406966*%i[C,R,R,L,L,R,L,L,L] 0.6817861497308*%i+0.3825328028943[C,R,R,L,R,L,L,L,L] 0.4143818300267-0.62346285089*%i[C,R,R,L,L,L,R,R,R] 0.8840811407218*%i-0.2482028526495[C,L,L,R,L,L,R,L,R] 0.4124704532661-0.6033739102922*%i[C,R,R,L,L,L,L,R,L] 0.7031843555246*%i+0.349592546398[C,R,L,L,R,R,R,L,L] 0.3604023053863-0.6149069810752*%i[C,R,R,L,R,L,R,R,L] 0.6952356300693*%i+0.3612494789529[C,R,R,L,R,R,L,R,L] 0.62346285089*%i+0.4143818300267[C,R,R,L,L,L,R,R,R] 0.6122595737352*%i+0.2628305450022[C,R,L,L,R,R,R,L,R] 0.6668193142791*%i+0.3826489179777[C,R,R,L,R,L,R,L,R] 0.6862355387979*%i+0.132543247674[C,R,L,L,R,L,L,R,R] 0.5586988406966*%i+0.4013069326432[C,R,R,L,L,R,L,L,L] 0.3636207176041-0.6646219888599*%i[C,R,R,L,R,R,R,R,L] 0.1560476300436-0.6601857031416*%i[C,R,L,L,R,R,L,R,L] 0.7016619075984*%i+0.3449219946171[C,R,L,L,R,R,R,R,R] 0.6149069810752*%i+0.3604023053863[C,R,R,L,R,L,R,R,L] 0.3806694095035-0.686012046204*%i[C,R,R,L,R,L,L,R,R] 0.349592546398-0.7031843555246*%i[C,R,L,L,R,R,R,L,L] 0.6033739102922*%i+0.4124704532661[C,R,R,L,L,L,L,R,L] 0.4173003829667-0.6193527462789*%i[C,R,R,L,L,L,R,L,L] 0.3825328028943-0.6817861497308*%i[C,R,R,L,R,L,L,L,L] 0.3449219946171-0.7016619075984*%i[C,R,L,L,R,R,R,R,R] 0.3826489179777-0.6668193142791*%i[C,R,R,L,R,L,R,L,R] 0.686012046204*%i+0.3806694095035[C,R,R,L,R,L,L,R,R] 0.6193527462789*%i+0.4173003829667[C,R,R,L,L,L,R,L,L] 0.3105669268303*%i-0.9225904880691[C,L,L,L,L,L,R,L,R] -0.3377149017377*%i-0.6723331748591[C,L,L,L,L,L,L,L,L] 0.3377149017377*%i-0.6723331748591[C,L,L,L,L,L,L,L,L] 0.7907831754064*%i-0.03155297481292[C,L,L,L,L,L,R,L,L] 0.4187640184497*%i-1.28923152775759[C,L,R,L,R,R,L,L,R] -0.8046356381701*%i-0.210705526779[C,L,L,R,L,L,R,L,L] -0.4780302565759*%i-0.6510137125767[C,L,L,L,L,L,L,R,L] 0.3612494789529-0.6952356300693*%i[C,R,R,L,R,R,L,R,L] -0.7907831754064*%i-0.03155297481292[C,L,L,L,L,L,R,L,L] 0.7016533637958*%i+0.3597833828653[C,R,L,L,R,R,L,L,R] 0.1609266721222*%i-1.42721606539989[C,L,R,L,L,L,R,R,R] 0.9841258499734*%i-0.02443174568138[C,L,L,R,L,L,L,L,R] 0.6124313544614*%i-0.6165326858499[C,L,L,L,L,R,L,L,R] 0.6865296971513*%i-0.6273252266385[C,L,L,L,L,R,R,R,L] 0.6852345690035*%i-0.6353565478646[C,L,L,L,L,R,R,R,R] 0.6707894613876*%i-0.3867064532748[C,L,L,R,L,L,L,L,R] 0.3358383724987*%i-1.15088834544671[C,L,R,L,R,L,L,L,R] 0.6866977063609*%i-0.5138736322601[C,L,L,R,L,R,L,R,L] 0.3726398086194*%i-1.02202326810287[C,L,L,L,R,L,R,R,L] 0.4780302565759*%i-0.6510137125767[C,L,L,L,L,L,L,R,L] 0.7040732663739*%i-0.5283268509101[C,L,L,R,L,R,L,R,R] 0.3927795742416*%i-1.03014582442919[C,L,L,L,R,L,R,R,R] 0.8046356381701*%i-0.210705526779[C,L,L,R,L,L,R,L,L] 0.8440854994406*%i-0.3035815498359[C,L,L,R,L,L,R,R,R] 0.03688601019766-0.8151298218686*%i[C,R,L,L,R,L,R,L,R] 0.8572357563587*%i+0.03019836885341[C,R,L,L,L,L,R,R,L] 0.8151298218686*%i+0.03688601019766[C,R,L,L,R,L,R,L,R] -0.6707894613876*%i-0.3867064532748[C,L,L,R,L,L,L,L,R] -0.667190207251*%i-0.5639672957349[C,L,L,L,L,R,L,L,L] -1.12028229191775*%i-0.205263236004[C,L,L,R,R,R,L,R,L] -0.7040732663739*%i-0.5283268509101[C,L,L,R,L,R,L,R,R] -1.09735312137974*%i-0.1912140829949[C,L,L,R,R,L,L,L,R] -0.8840811407218*%i-0.2482028526495[C,L,L,R,L,L,R,L,R] -0.6866977063609*%i-0.5138736322601[C,L,L,R,L,R,L,R,L] -0.8533203996892*%i-0.2884576859573[C,L,L,R,L,L,R,R,L] -0.8440854994406*%i-0.3035815498359[C,L,L,R,L,L,R,R,R] -1.02011353852853*%i-0.1294463768282[C,L,L,R,L,L,L,R,L] 0.03019836885341-0.8572357563587*%i[C,R,L,L,L,L,R,R,L] -0.4721945038287*%i-0.7064983534592[C,L,L,L,L,L,L,R,R] -0.6708934980973*%i-0.618913749691[C,L,L,L,L,R,R,L,L] 0.4721945038287*%i-0.7064983534592[C,L,L,L,L,L,L,R,R] -0.6124313544614*%i-0.6165326858499[C,L,L,L,L,R,L,L,R] 0.870659713648*%i+0.02698848255358[C,R,L,L,L,L,R,R,R] 0.02698848255358-0.870659713648*%i[C,R,L,L,L,L,R,R,R] 0.6708934980973*%i-0.618913749691[C,L,L,L,L,R,R,L,L] -1.02659815729454*%i-0.01303925298338[C,L,L,R,L,R,R,L,L] 0.6916283341584*%i-0.6043996879657[C,L,L,L,L,R,R,L,R] -0.6865296971513*%i-0.6273252266385[C,L,L,L,L,R,R,R,L] -0.6916283341584*%i-0.6043996879657[C,L,L,L,L,R,R,L,R] -1.01168377420407*%i-0.01788175151935[C,L,L,R,L,R,L,L,L] -0.6852345690035*%i-0.6353565478646[C,L,L,L,L,R,R,R,R] -1.10476361681278*%i-0.1522702900574[C,L,L,R,R,L,R,L,R] -1.03064681818891*%i-0.008101810724996[C,L,L,R,L,R,R,L,R] -1.00131205939037*%i-4.341424825955528E-4[C,L,L,R,L,R,L,R,L] -0.9943595314843*%i-0.06224793007082[C,L,L,R,L,R,L,L,R] -1.03627050179761*%i-0.01387405910814[C,L,L,R,L,R,R,R,L] 0.9239995237753*%i-0.1054699381674[C,L,L,R,L,L,L,L,L] -0.9239995237753*%i-0.1054699381674[C,L,L,R,L,L,L,L,L] 0.8533203996892*%i-0.2884576859573[C,L,L,R,L,L,R,R,L] 1.03757447488346*%i-0.01655619739513[C,L,L,R,L,R,R,R,R] 1.08971502362741*%i-0.1707170867676[C,L,L,R,R,L,L,L,L] 1.10346030870066*%i-0.1589192302653[C,L,L,R,R,L,R,L,L] -0.3105669268303*%i-0.9225904880691[C,L,L,L,L,L,R,L,R] 1.11377591360615*%i-0.212135023293[C,L,L,R,R,R,L,L,L] 1.00131205939037*%i-4.341424825955528E-4[C,L,L,R,L,R,L,R,L] 1.03627050179761*%i-0.01387405910814[C,L,L,R,L,R,R,R,L] 1.03064681818891*%i-0.008101810724996[C,L,L,R,L,R,R,L,R] 1.09735312137974*%i-0.1912140829949[C,L,L,R,R,L,L,L,R] 0.4171097614545*%i-1.23937100844723[C,L,R,L,R,R,L,R,R] 1.10476361681278*%i-0.1522702900574[C,L,L,R,R,L,R,L,R] -0.9841258499734*%i-0.02443174568138[C,L,L,R,L,L,L,L,R] 0.9943595314843*%i-0.06224793007082[C,L,L,R,L,R,L,L,R] 1.11179052208332*%i-0.1564236091309[C,L,L,R,R,L,R,R,L] 0.002092404656038-1.00599025776942*%i[C,R,L,R,L,R,L,R,R] 1.10358376955829*%i-0.2043601123214[C,L,L,R,R,R,L,L,R] 1.05348392125708*%i-0.1820609329886[C,L,L,R,R,L,L,R,L] -1.08971502362741*%i-0.1707170867676[C,L,L,R,R,L,L,L,L] 1.11962364630875*%i-0.2224810035929[C,L,L,R,R,R,R,L,R] -1.11179052208332*%i-0.1564236091309[C,L,L,R,R,L,R,R,L] -0.1881744766231*%i-1.2751472213804[C,L,R,L,R,L,R,L,R] -1.05348392125708*%i-0.1820609329886[C,L,L,R,R,L,L,R,L] 1.1168474817201*%i-0.2267931108976[C,L,L,R,R,R,R,R,L] 1.11356032999583*%i-0.1583273513176[C,L,L,R,R,L,R,R,R] -0.3726398086194*%i-1.02202326810287[C,L,L,L,R,L,R,R,L] 1.12028229191775*%i-0.205263236004[C,L,L,R,R,R,L,R,L] 1.00599025776942*%i+0.002092404656038[C,R,L,R,L,R,L,R,R] 1.01168377420407*%i-0.01788175151935[C,L,L,R,L,R,L,L,L] 1.02011353852853*%i-0.1294463768282[C,L,L,R,L,L,L,R,L] -1.11377591360615*%i-0.212135023293[C,L,L,R,R,R,L,L,L] -0.3927795742416*%i-1.03014582442919[C,L,L,L,R,L,R,R,R] -0.3236363068336*%i-1.24176519152419[C,L,R,L,R,L,L,L,L] -1.12241968878209*%i-0.2070185711871[C,L,L,R,R,R,L,R,R] -1.10358376955829*%i-0.2043601123214[C,L,L,R,R,R,L,L,R] -1.01912960226129*%i-0.1818322311253[C,L,L,R,R,L,L,R,R] 1.11582942315977*%i-0.2215095740009[C,L,L,R,R,R,R,L,L] 1.01912960226129*%i-0.1818322311253[C,L,L,R,R,L,L,R,R] -1.05137823107872*%i-0.1433247000985[C,L,L,R,L,L,L,R,R] 1.02659815729454*%i-0.01303925298338[C,L,L,R,L,R,R,L,L] 0.03509510980141*%i-1.62889136284479[C,L,R,L,L,R,L,R,R] -1.03757447488346*%i-0.01655619739513[C,L,L,R,L,R,R,R,R] -0.3484548330034*%i-1.03952871434722[C,L,L,L,R,L,R,L,L] -0.3554893766182*%i-1.26744336685605[C,L,R,L,R,L,L,R,L] -0.3358383724987*%i-1.15088834544671[C,L,R,L,R,L,L,L,R] 2.031393048282539E-47*%i-1.93224396657609[C,L,R,R,L,L,R,R,L] 1.05137823107872*%i-0.1433247000985[C,L,L,R,L,L,L,R,R] -1.11356032999583*%i-0.1583273513176[C,L,L,R,R,L,R,R,R] 0.3484548330034*%i-1.03952871434722[C,L,L,L,R,L,R,L,L] -1.10346030870066*%i-0.1589192302653[C,L,L,R,R,L,R,L,L] -1.11546788192986*%i-0.2280038019212[C,L,L,R,R,R,R,R,R] -1.11582942315977*%i-0.2215095740009[C,L,L,R,R,R,R,L,L] 1.11546788192986*%i-0.2280038019212[C,L,L,R,R,R,R,R,R] -1.1168474817201*%i-0.2267931108976[C,L,L,R,R,R,R,R,L] 1.12241968878209*%i-0.2070185711871[C,L,L,R,R,R,L,R,R] -1.11962364630875*%i-0.2224810035929[C,L,L,R,R,R,R,L,R] -0.1471010239722*%i-1.41470923490948[C,L,R,L,L,L,R,R,L] -0.1609266721222*%i-1.42721606539989[C,L,R,L,L,L,R,R,R] -0.1193502520189*%i-1.40005273575979[C,L,R,L,L,L,R,L,L] -0.435870402829*%i-1.29157545679914[C,L,R,L,R,R,R,L,L] -0.4353370502396*%i-1.28186685388729[C,L,R,L,R,R,R,L,R] -0.03721455090825*%i-1.48587713103903[C,L,R,L,L,L,L,L,R] -1.467863341863332E-45*%i-1.99858658884221[C,L,R,R,R,R,R,L,L] -0.403918284086*%i-1.25127157362703[C,L,R,L,R,R,L,R,L] 0.435870402829*%i-1.29157545679914[C,L,R,L,R,R,R,L,L] 0.1471010239722*%i-1.41470923490948[C,L,R,L,L,L,R,R,L] 0.4353370502396*%i-1.28186685388729[C,L,R,L,R,R,R,L,R] 1.601472564789338E-63*%i-1.55528270076858[C,L,R,L,L,L,L,L,L] -0.03509510980141*%i-1.62889136284479[C,L,R,L,L,R,L,R,R] -1.756946891014356E-45*%i-1.99037638105595[C,L,R,R,R,R,L,R,L] -0.4147002145052*%i-1.26920435475802[C,L,R,L,R,R,L,L,L] 0.3526670352836*%i-1.29262582414273[C,L,R,L,R,L,L,R,R] -1.098822311635797E-61*%i-1.59568096343975[C,L,R,L,L,L,L,R,L] -7.000410530976591E-58*%i-1.69014226311886[C,L,R,L,L,R,L,L,L] 0.06558445162322*%i-1.77110876373285[C,L,R,R,L,R,R,R,R] -0.4187640184497*%i-1.28923152775759[C,L,R,L,R,R,L,L,R] 0.4147002145052*%i-1.26920435475802[C,L,R,L,R,R,L,L,L] -0.4399419047236*%i-1.29340668859999[C,L,R,L,R,R,R,R,L] 0.060847287392*%i-1.76996979936662[C,L,R,R,L,R,R,R,L] -1.960797024110329E-45*%i-1.99541903266131[C,L,R,R,R,R,L,L,R] 0.05142235910285*%i-1.76835884404877[C,L,R,R,L,R,R,L,L] -0.4416274255857*%i-1.29600138117043[C,L,R,L,R,R,R,R,R] 3.796573762224404E-59*%i-1.65613256257421[C,L,R,L,L,R,L,R,L] -2.826068607232113E-46*%i-1.96402433682015[C,L,R,R,R,L,R,L,R] 0.1193502520189*%i-1.40005273575979[C,L,R,L,L,L,R,L,L] 0.3554893766182*%i-1.26744336685605[C,L,R,L,R,L,L,R,L] 0.1881744766231*%i-1.2751472213804[C,L,R,L,R,L,R,L,R] 0.3236363068336*%i-1.24176519152419[C,L,R,L,R,L,L,L,L] 0.403918284086*%i-1.25127157362703[C,L,R,L,R,R,L,R,L] -0.4171097614545*%i-1.23937100844723[C,L,R,L,R,R,L,R,R] 0.4416274255857*%i-1.29600138117043[C,L,R,L,R,R,R,R,R] -0.3526670352836*%i-1.29262582414273[C,L,R,L,R,L,L,R,R] -1.367787997710478E-45*%i-1.98381024999972[C,L,R,R,R,L,L,R,R] 1.921789396948007E-45*%i-1.99313025487898[C,L,R,R,R,R,L,L,L] 8.97131366742683E-46*%i-1.97945750485595[C,L,R,R,R,L,L,R,L] -3.341064195751925E-46*%i-1.99994352176567[C,L,R,R,R,R,R,R,R] 1.584869273343095E-46*%i-1.9573250505357[C,L,R,R,R,L,R,L,L] -6.2929329733245E-46*%i-1.97478085890012[C,L,R,R,R,L,L,L,L] 1.669245819083336E-45*%i-1.98700434751505[C,L,R,R,R,R,L,R,R] 0.006634804929479*%i-1.94151226502158[C,L,R,R,R,L,R,R,R] 0.008033588863739*%i-1.86142786012481[C,L,R,R,L,L,L,R,R] -1.223649387459974E-48*%i-1.9031167730156[C,L,R,R,L,L,L,L,R] 4.361209781584072E-46*%i-1.9694191207309[C,L,R,R,R,L,L,L,R] -3.493899424805764E-52*%i-1.82275632249229[C,L,R,R,L,R,L,L,L] 9.602348077312813E-46*%i-1.9994914380164[C,L,R,R,R,R,R,R,L] 2.456734993573938E-51*%i-1.84128856150969[C,L,R,R,L,R,L,R,L] 0.4399419047236*%i-1.29340668859999[C,L,R,L,R,R,R,R,L] -0.01379614336949*%i-1.7577830600831[C,L,R,R,L,R,R,L,R] 2.70631446576374E-53*%i-1.78586564641067[C,L,R,R,L,R,L,L,R] 0.01379614336949*%i-1.7577830600831[C,L,R,R,L,R,R,L,R] -0.06558445162322*%i-1.77110876373285[C,L,R,R,L,R,R,R,R] 0.03721455090825*%i-1.48587713103903[C,L,R,L,L,L,L,L,R] -1.003224969291492E-49*%i-1.8783826015001[C,L,R,R,L,L,L,R,L] -6.645959912397407E-48*%i-1.9222857782463[C,L,R,R,L,L,R,L,L] -0.008033588863739*%i-1.86142786012481[C,L,R,R,L,L,L,R,R] 3.150007509803307E-49*%i-1.89077542436024[C,L,R,R,L,L,L,L,L] 2.743218129014354E-48*%i-1.91144463147345[C,L,R,R,L,L,R,L,R] -0.05142235910285*%i-1.76835884404877[C,L,R,R,L,R,R,L,L] -0.006634804929479*%i-1.94151226502158[C,L,R,R,R,L,R,R,R] -0.060847287392*%i-1.76996979936662[C,L,R,R,L,R,R,R,L] -9.742372387692846E-47*%i-1.94957490324939[C,L,R,R,R,L,R,R,L] 1.815599252500064E-45*%i-1.99722302469658[C,L,R,R,R,R,R,L,R] ---------------------------------------------------- ------------------------------------------------------- ---------------------------------------------------- ---------------------------------------------------------- period =10 c = 0.4736182403427*%i-0.7112999953742[C,L,L,L,L,L,L,R,R,R] 0.05413745194802*%i+0.3296899051038[C,R,R,R,R,R,R,R,R,L] 0.4700481533889-0.3475095636666*%i[C,R,R,R,L,L,L,L,L,R] 0.3296899051038-0.05413745194802*%i[C,R,R,R,R,R,R,R,R,L] 0.3568172484923-0.06945286546683*%i[C,R,R,R,R,R,R,R,L,R] 0.2359297942232*%i+0.4490790647371[C,R,R,R,R,L,R,L,L,R] 0.09104344010005*%i+0.3787904573762[C,R,R,R,R,R,R,L,L,L] 0.06945286546683*%i+0.3568172484923[C,R,R,R,R,R,R,R,L,R] 0.3849307779412-0.102534284662*%i[C,R,R,R,R,R,R,L,R,R] 0.102534284662*%i+0.3849307779412[C,R,R,R,R,R,R,L,R,R] 0.1351595039424*%i+0.4108658438278[C,R,R,R,R,R,L,L,L,R] 0.3787904573762-0.09104344010005*%i[C,R,R,R,R,R,R,L,L,L] 0.4108658438278-0.1351595039424*%i[C,R,R,R,R,R,L,L,L,R] 0.4032314575033-0.1297517858374*%i[C,R,R,R,R,R,L,L,R,L] 0.1297517858374*%i+0.4032314575033[C,R,R,R,R,R,L,L,R,L] 0.4156154401242-0.1490359148832*%i[C,R,R,R,R,R,L,R,L,L] 0.2500984349698*%i+0.4414903669736[C,R,R,R,R,L,R,R,R,R] 0.245606834143*%i+0.4461186830635[C,R,R,R,R,L,R,R,L,L] 0.1490359148832*%i+0.4156154401242[C,R,R,R,R,R,L,R,L,L] 0.2000962882521*%i+0.4368000686686[C,R,R,R,R,L,L,R,L,R] 0.4085181851161-0.3400380641374*%i[C,R,R,R,L,L,R,R,R,L] 0.4146858430175-0.1577259882724*%i[C,R,R,R,R,R,L,R,R,R] 0.2308621468216*%i+0.4465547112177[C,R,R,R,R,L,R,L,R,L] 0.1577259882724*%i+0.4146858430175[C,R,R,R,R,R,L,R,R,R] 0.4444158435492-0.2089026797061*%i[C,R,R,R,R,L,L,L,L,L] 0.4455767395399-0.2137535396522*%i[C,R,R,R,R,L,L,L,R,R] 0.4368000686686-0.2000962882521*%i[C,R,R,R,R,L,L,R,L,R] 0.2137535396522*%i+0.4455767395399[C,R,R,R,R,L,L,L,R,R] 0.4262491629822-0.1983573234186*%i[C,R,R,R,R,L,L,R,R,L] 0.2089026797061*%i+0.4444158435492[C,R,R,R,R,L,L,L,L,L] 0.4465547112177-0.2308621468216*%i[C,R,R,R,R,L,R,L,R,L] 0.1983573234186*%i+0.4262491629822[C,R,R,R,R,L,L,R,R,L] 0.4490790647371-0.2359297942232*%i[C,R,R,R,R,L,R,L,L,R] 0.4461186830635-0.245606834143*%i[C,R,R,R,R,L,R,R,L,L] 0.3539163310389*%i+0.4703414190983[C,R,R,R,L,L,L,R,L,L] 0.3400380641374*%i+0.4085181851161[C,R,R,R,L,L,R,R,R,L] 0.3568961858171*%i+0.4688608656795[C,R,R,R,L,L,L,R,R,R] 0.4414903669736-0.2500984349698*%i[C,R,R,R,R,L,R,R,R,R] 0.4336572757654*%i+0.3519179541884[C,R,R,L,L,R,R,R,L,R] 0.3186603057905*%i+0.4418005288922[C,R,R,R,L,L,R,R,L,R] 0.4568579604318-0.3265774077188*%i[C,R,R,R,L,L,R,L,L,L] 0.4418005288922-0.3186603057905*%i[C,R,R,R,L,L,R,R,L,R] 0.3943574349319*%i+0.4648022915858[C,R,R,R,L,R,L,L,R,R] 0.3915341432705*%i+0.4656359840129[C,R,R,R,L,R,L,L,L,L] 0.4076919421627*%i+0.4564854661547[C,R,R,R,L,R,R,L,L,R] 0.3840704417759*%i+0.4643008567474[C,R,R,R,L,R,L,R,L,R] 0.3805188223667*%i+0.4577073312693[C,R,R,R,L,R,L,R,R,L] 0.3451176852131*%i+0.4667341248586[C,R,R,R,L,L,L,L,R,L] 0.3306799608497*%i+0.4601183520785[C,R,R,R,L,L,R,L,R,R] 0.4688608656795-0.3568961858171*%i[C,R,R,R,L,L,L,R,R,R] 0.4601183520785-0.3306799608497*%i[C,R,R,R,L,L,R,L,R,R] 0.3265774077188*%i+0.4568579604318[C,R,R,R,L,L,R,L,L,L] 0.4703414190983-0.3539163310389*%i[C,R,R,R,L,L,L,R,L,L] 0.4577073312693-0.3805188223667*%i[C,R,R,R,L,R,L,R,R,L] 0.4111444258221*%i+0.4501427343275[C,R,R,R,L,R,R,R,L,L] 0.4667341248586-0.3451176852131*%i[C,R,R,R,L,L,L,L,R,L] 0.6467175587471*%i+0.3571821390763[C,R,R,L,R,R,R,R,L,R] 0.3475095636666*%i+0.4700481533889[C,R,R,R,L,L,L,L,L,R] 0.4648022915858-0.3943574349319*%i[C,R,R,R,L,R,L,L,R,R] 0.506850511814*%i+0.3582043914715[C,R,R,L,L,R,R,L,L,L] 0.3519179541884-0.4336572757654*%i[C,R,R,L,L,R,R,R,L,R] 0.4070924182505-0.6063670966516*%i[C,R,R,L,L,L,L,R,R,L] 0.382466905443-0.664537110006*%i[C,R,R,L,R,L,R,L,L,L] 0.4168976616949-0.6176244941696*%i[C,R,R,L,L,L,R,L,R,L] 0.3664633425652-0.6764885397393*%i[C,R,R,L,R,R,L,R,R,L] 0.4501427343275-0.4111444258221*%i[C,R,R,R,L,R,R,R,L,L] 0.4656359840129-0.3915341432705*%i[C,R,R,R,L,R,L,L,L,L] 0.4570178801339-0.4036782648474*%i[C,R,R,R,L,R,R,L,R,L] 0.4459244510111-0.4109755346715*%i[C,R,R,R,L,R,R,R,R,R] 0.3510163239117-0.7021266614959*%i[C,R,L,L,R,R,R,L,R,L] 0.4643008567474-0.3840704417759*%i[C,R,R,R,L,R,L,R,L,R] 0.4109755346715*%i+0.4459244510111[C,R,R,R,L,R,R,R,R,R] 0.4564854661547-0.4076919421627*%i[C,R,R,R,L,R,R,L,L,R] 0.3704848200226-0.5232955977234*%i[C,R,R,L,L,R,R,L,R,R] 0.4036782648474*%i+0.4570178801339[C,R,R,R,L,R,R,L,R,L] 0.05027183482336-0.6304685522939*%i[C,R,L,L,R,L,L,R,L,L] 0.3582043914715-0.506850511814*%i[C,R,R,L,L,R,R,L,L,L] 0.6304685522939*%i+0.05027183482336[C,R,L,L,R,L,L,R,L,L] 0.6209132651989*%i+0.2530077896631[C,R,L,L,R,R,R,L,R,R] 0.7012235654377*%i+0.360741931728[C,R,L,L,R,R,L,L,L,L] 0.5232955977234*%i+0.3704848200226[C,R,R,L,L,R,R,L,R,R] 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0.6867074513832*%i+0.3802186896568[C,R,R,L,R,R,L,R,R,R] 0.66694342722*%i+0.1613136862645[C,R,L,L,R,R,L,L,L,R] 0.4081476650666-0.5659603705082*%i[C,R,R,L,L,R,L,R,L,L] 0.1613136862645-0.66694342722*%i[C,R,L,L,R,R,L,L,L,R] 0.5699056125524*%i+0.408387746098[C,R,R,L,L,R,L,R,R,R] 0.3812377933632-0.5993780979424*%i[C,R,R,L,L,L,R,R,R,L] 0.1394959551968-0.6847796698734*%i[C,R,L,L,R,R,L,R,R,L] 0.6926868340029*%i+0.3570294646971[C,R,R,L,R,R,R,R,R,L] 0.6200046310192*%i+0.4181131378143[C,R,R,L,L,L,R,L,L,R] 0.6822534548036*%i+0.383452503106[C,R,R,L,R,L,L,L,L,R] 0.7021266614959*%i+0.3510163239117[C,R,L,L,R,R,R,L,R,L] 0.6087782507921*%i+0.4198376793883[C,R,R,L,L,L,L,L,R,R] 0.1294789834418-0.6907733888588*%i[C,R,L,L,R,L,L,R,R,R] 0.6233581126222*%i+0.4155144811531[C,R,R,L,L,L,R,R,L,L] 0.981944785759*%i-0.01995775591606[C,L,L,R,L,L,L,L,R,R] 0.5659603705082*%i+0.4081476650666[C,R,R,L,L,R,L,R,L,L] 0.624197310616*%i+0.4136468549112[C,R,R,L,L,L,R,R,R,R] 0.7011964670056*%i+0.344044971167[C,R,L,L,R,R,R,R,R,R] 0.6907733888588*%i+0.1294789834418[C,R,L,L,R,L,L,R,R,R] 0.360741931728-0.7012235654377*%i[C,R,L,L,R,R,L,L,L,L] 0.4155144811531-0.6233581126222*%i[C,R,R,L,L,L,R,R,L,L] 0.3571821390763-0.6467175587471*%i[C,R,R,L,R,R,R,R,L,R] 0.6680010897272*%i+0.3838508958703[C,R,R,L,R,L,R,L,R,R] 0.4198376793883-0.6087782507921*%i[C,R,R,L,L,L,L,L,R,R] 0.4191936114374-0.6066740987122*%i[C,R,R,L,L,L,L,L,L,L] 0.6847796698734*%i+0.1394959551968[C,R,L,L,R,R,L,R,R,L] 0.4143362110144-0.6015473814931*%i[C,R,R,L,L,L,L,R,L,R] 0.664537110006*%i+0.382466905443[C,R,R,L,R,L,R,L,L,L] 0.6015473814931*%i+0.4143362110144[C,R,R,L,L,L,L,R,L,R] 0.3838508958703-0.6680010897272*%i[C,R,R,L,R,L,R,L,R,R] 0.383452503106-0.6822534548036*%i[C,R,R,L,R,L,L,L,L,R] 0.4136468549112-0.624197310616*%i[C,R,R,L,L,L,R,R,R,R] 0.3631734895689-0.6960394334179*%i[C,R,R,L,R,R,L,R,L,R] 0.3815821071188-0.6857221174851*%i[C,R,R,L,R,L,L,R,L,L] 0.3492967686749-0.7041370677221*%i[C,R,L,L,R,R,R,L,L,R] 0.8988376454083*%i-0.06083594480108[C,L,L,R,L,L,R,L,L,R] 0.6066740987122*%i+0.4191936114374[C,R,R,L,L,L,L,L,L,L] 0.3560151535565*%i-0.7210023708577[C,L,L,L,L,L,L,L,L,R] 0.6176244941696*%i+0.4168976616949[C,R,R,L,L,L,R,L,R,L] 0.8861731762313*%i-0.2518130438055[C,L,L,R,R,L,R,L,R,R] 0.7586385625538*%i+0.0118013362497[C,R,L,L,R,L,L,L,L,R] 0.3816211131657-0.6801437365798*%i[C,R,R,L,R,L,L,L,R,L] 0.4181131378143-0.6200046310192*%i[C,R,R,L,L,L,R,L,L,R] 0.6764885397393*%i+0.3664633425652[C,R,R,L,R,R,L,R,R,L] 0.3570294646971-0.6926868340029*%i[C,R,R,L,R,R,R,R,R,L] 0.3453825501406-0.7026889089485*%i[C,R,L,L,R,R,R,R,L,L] 0.0118013362497-0.7586385625538*%i[C,R,L,L,R,L,L,L,L,R] 0.6704340726514*%i-0.3611140718002[C,L,L,R,L,L,L,L,R,L] 1.11617448912675*%i-0.2262665140262[C,L,L,R,R,R,R,R,L,L] 0.6799419786982*%i-0.3953074362583[C,L,L,R,L,L,L,L,R,R] -0.247048121274*%i-0.9192785452441[C,L,L,L,L,L,L,L,R,L] 0.8410871304367*%i-0.2840556075226[C,L,L,R,L,L,R,R,L,L] 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0.02593307974659*%i-1.74158409922802[C,L,R,L,L,R,R,L,R,R] -0.05572268594288*%i-1.76987732307224[C,L,R,R,L,R,R,L,L,R] -0.0349342387714*%i-1.76541034825413[C,L,R,R,L,R,R,L,R,L] 0.02955133822421*%i-1.6283340764918[C,L,R,L,L,R,L,R,R,L] -2.533378473093587E-111*%i-1.72191509958869[C,L,R,L,L,R,L,L,R,L] -0.04672360651812*%i-1.76732270021644[C,L,R,R,L,R,R,L,L,L] 0.005732131804038*%i-1.67438538719966[C,L,R,L,L,R,L,L,L,R] 7.495474091865462E-105*%i-1.80243613481171[C,L,R,R,L,R,L,L,R,L] -0.02593307974659*%i-1.74158409922802[C,L,R,L,L,R,R,L,R,R] -0.005732131804038*%i-1.67438538719966[C,L,R,L,L,R,L,L,L,R] 6.732247454850615E-103*%i-1.82950962395645[C,L,R,R,L,R,L,L,L,R] 4.900367455481059E-102*%i-1.84662721119897[C,L,R,R,L,R,L,R,L,L] -5.721136929836905E-104*%i-1.8162948552384[C,L,R,R,L,R,L,L,L,L] -0.02955133822421*%i-1.6283340764918[C,L,R,L,L,R,L,R,R,L] -2.786137864330104E-96*%i-1.9144798636784[C,L,R,R,L,L,R,L,R,L] -0.06269499333468*%i-1.77046612534542[C,L,R,R,L,R,R,R,L,L] 0.001985091966513*%i-1.90735179165188[C,L,R,R,L,L,R,L,R,R] -0.06601242506922*%i-1.77121666387233[C,L,R,R,L,R,R,R,R,R] -1.560163215883432E-102*%i-1.83515884526123[C,L,R,R,L,R,L,R,L,R] -0.0101006805949*%i-1.86157227509445[C,L,R,R,L,L,L,R,R,R] -0.001985091966513*%i-1.90735179165188[C,L,R,R,L,L,R,L,R,R] -8.505398105376345E-101*%i-1.86155841375373[C,L,R,R,L,L,L,R,R,L] -1.151615858226028E-90*%i-1.99828890735048[C,L,R,R,R,R,R,L,L,L] -5.194726189536907E-99*%i-1.882407933754[C,L,R,R,L,L,L,R,L,R] 1.599932675229161E-97*%i-1.89983233779156[C,L,R,R,L,L,L,L,R,L] 1.097437691607356E-90*%i-1.99885576598122[C,L,R,R,R,R,R,L,L,R] -1.852934014116263E-94*%i-1.93539073477253[C,L,R,R,L,L,R,R,L,L] 1.44101256638539E-98*%i-1.8871722063977[C,L,R,R,L,L,L,L,L,R] 7.120351194188842E-96*%i-1.91963548931856[C,L,R,R,L,L,R,L,L,L] -4.708652132114346E-98*%i-1.8940020228605[C,L,R,R,L,L,L,L,L,L] -2.122756607425653E-92*%i-1.96582178550208[C,L,R,R,R,L,R,L,R,R] 0.005019022586386*%i-1.94141455218956[C,L,R,R,R,L,R,R,R,L] 5.238174495963794E-95*%i-1.92932033094495[C,L,R,R,L,L,R,R,L,R] 5.940162791639009E-91*%i-1.99374786424605[C,L,R,R,R,R,L,L,L,L] 0.3536624997012*%i-1.28902550873216[C,L,R,L,R,L,L,R,R,L] -0.1620793249109*%i-1.42826401830112[C,L,R,L,L,L,R,R,R,R] -0.1480503143153*%i-1.4015679539071[C,L,R,L,L,L,R,R,L,R] -0.3536624997012*%i-1.28902550873216[C,L,R,L,R,L,L,R,R,L] -1.71614037609385E-119*%i-1.62943250044632[C,L,R,L,L,R,L,R,L,L] 1.556854816772446E-127*%i-1.53624327128231[C,L,R,L,L,L,L,L,L,L] -0.03776980210038*%i-1.6291647140729[C,L,R,L,L,R,L,R,R,R] -0.01103329438785*%i-1.57519864434807[C,L,R,L,L,L,L,R,L,R] -2.733268108734224E-130*%i-1.50171683940963[C,L,R,L,L,L,L,L,R,L] 0.01103329438785*%i-1.57519864434807[C,L,R,L,L,L,L,R,L,R] 3.984896434293403E-135*%i-1.44700884060748[C,L,R,L,L,L,R,L,R,L] 3.456338601389611E-92*%i-1.973497417322[C,L,R,R,R,L,L,L,L,L] -4.379141280659597E-92*%i-1.97604216861176[C,L,R,R,R,L,L,L,L,R] 2.963033425724338E-91*%i-1.991120876123[C,L,R,R,R,R,L,R,L,R] -2.686228055029422E-92*%i-1.97085788910142[C,L,R,R,R,L,L,L,R,L] 4.925893945255516E-92*%i-1.97829335447698[C,L,R,R,R,L,L,R,L,R] -1.076429893860896E-90*%i-1.99680455274246[C,L,R,R,R,R,R,L,R,R] 2.704599350856663E-92*%i-1.96774277629347[C,L,R,R,R,L,L,L,R,R] -4.811665097267764E-92*%i-1.98057717342423[C,L,R,R,R,L,L,R,L,L] -7.619784768205814E-91*%i-1.99488919935077[C,L,R,R,R,R,L,L,R,L] 9.305151221106146E-93*%i-1.96237868970248[C,L,R,R,R,L,R,L,R,L] 3.981315319777683E-92*%i-1.98271940829787[C,L,R,R,R,L,L,R,R,L] -1.747804379017484E-91*%i-1.98960058691205[C,L,R,R,R,R,L,R,L,L] -5.816435501760556E-93*%i-1.9590980465523[C,L,R,R,R,L,R,L,L,L] 7.507359880159295E-91*%i-1.99964691773327[C,L,R,R,R,R,R,R,L,L] 3.734167000398599E-93*%i-1.95542332702632[C,L,R,R,R,L,R,L,L,R] -3.985829909476627E-92*%i-1.98548232097316[C,L,R,R,R,R,L,R,R,R] -1.99247938217849 [C,L,R,R,R,R,L,L,L,R] -1.94687345417958 [C,L,R,R,R,L,R,R,L,L] -1.99930750428061 [C,L,R,R,R,R,R,R,L,R] -1.95189999687375 [C,L,R,R,R,L,R,R,L,R] -1.98794057428053 [C,L,R,R,R,R,L,R,R,L] -0.007428373822976*%i-1.94156904855457 [C,L,R,R,R,L,R,R,R,R] -1.99998588114039 [C,L,R,R,R,R,R,R,R,R] -0.005019022586386*%i-1.94141455218956 [C,L,R,R,R,L,R,R,R,L] -1.99760809386352 [C,L,R,R,R,R,R,L,R,L] -1.99987291176633 [C,L,R,R,R,R,R,R,R,L] -1.92503423850107 [C,L,R,R,L,L,R,L,L,R] -1.99592415193075 [C,L,R,R,R,R,L,L,R,R] ================================================================================ /* Maxima batch script for periods >=10 run from console or XMaxima, not wxMaxima for example from console under windows run: cd C:\Program Files\Maxima-5.16.3\bin maxima batch("D:/doc/programming/maxima/batch/MandelbrotCenters/sequence/center_seq_new.mac")$ */ start:elapsed_run_time (); load(cpoly); period:10; /* basic funtion = monic and centered complex quadratic polynomial http://en.wikipedia.org/wiki/Complex_quadratic_polynomial */ f(z,c):=z*z+c $ /* iterated function */ fn(n, z, c) := if n=1 then f(z,c) else f(fn(n-1, z, c),c) $ /* roots of Fn are periodic point of fn function */ Fn(n,z,c):=fn(n, z, c)-z $ /* gives irreducible divisors of polynomial Fn[p,z=0,c] */ GiveG[p]:= block( [f:divisors(p),t:1], g, f:delete(p,f), if p=1 then return(Fn(p,0,c)), for i in f do t:t*GiveG[i], g: Fn(p,0,c)/t, return(ratsimp(g)) )$ /* use : load(cpoly); roots:GiveRoots_bf(GiveG[3]); */ GiveRoots_bf(g):= block( [cc:bfallroots(expand(%i*g)=0)], cc:map(rhs,cc),/* remove string "c=" */ return(cc) )$ GiveCenters_bf(p):= block( [g, cc:[]], fpprintprec:15, /* number of digits to display */ if p<7 then fpprec:16 elseif p=7 then fpprec:40 elseif p=8 then fpprec:70 elseif p=9 then fpprec:150 elseif p=10 then fpprec:300, g:GiveG[p], cc:GiveRoots_bf(g), return(cc) ); /* Gives symbolic sequence of critical point z_cr=0 of length iMax */ GiveSequence(c,iMax):= block( [s:[C], z:0], for i:1 thru iMax-1 step 1 do (z:f(z,c), if cabs(z)<0.0001 then s:append(s,[C]) /* z=z_cr=0 */ elseif realpart(z)>0 then s:append(s,[R]) elseif realpart(z)<0 then s:append(s,[L]) ), return(s) ); cs:[period]; centers[period]:GiveCenters_bf(period); for c in centers[period] do ( s:GiveSequence(c,period), disp(c,s), cs:sconcat(cs,float(c),s) ); stringout("centers_string.txt",cs);