Result of recursively taking log of a quaternion in Julia

QuaternionLog.jl

recursive_func(q, 100, log)

Quaternion{Float64}(0.0, 0.2138427021361156, 0.6498259226581785, 0.04673029529787405, false)
Quaternion{Float64}(-0.37731329782035117, 0.489868364488579, 1.4886136340169336, 0.10704921468429084, false)
Quaternion{Float64}(0.4796303624933924, 0.5633858732517517, 1.7120188869731483, 0.12311473789246809, false)
Quaternion{Float64}(0.6254684847358931, 0.40893747680176057, 1.242680580247547, 0.0893636717943734, false)
Quaternion{Float64}(0.3735054584912868, 0.35106899793994956, 1.066829652001861, 0.07671787617620018, false)
Quaternion{Float64}(0.1706470491382181, 0.3899604970562924, 1.1850132703548995, 0.08521669900311565, false)
Quaternion{Float64}(0.2327178376780377, 0.44757009502094197, 1.360077510459367, 0.09780592228727658, false)
Quaternion{Float64}(0.37425627242318393, 0.4397353421632598, 1.3362692371178646, 0.09609382123838361, false)
Quaternion{Float64}(0.3776581104899513, 0.40895937970377383, 1.2427471388598696, 0.08936845815869039, false)
Quaternion{Float64}(0.31090093152853704, 0.40242197459078016, 1.2228812502094477, 0.0879398619598939, false)
Quaternion{Float64}(0.2831608568053628, 0.4161356905635626, 1.264554536443051, 0.09093667218833638, false)
Quaternion{Float64}(0.3104808513233154, 0.42465717422354976, 1.2904496496568891, 0.09279884210963556, false)
Quaternion{Float64}(0.3340695336036758, 0.41995607134023355, 1.2761639223996764, 0.09177152659328365, false)
Quaternion{Float64}(0.32745828905964813, 0.41403302039710715, 1.2581649352674498, 0.09047718305538509, false)
Quaternion{Float64}(0.3129203889966859, 0.4144534937312651, 1.25944267104984, 0.09056906761760679, false)
Quaternion{Float64}(0.311386355942643, 0.4177513693201955, 1.2694642664841538, 0.09128974079741105, false)
Quaternion{Float64}(0.3186456968788053, 0.41863957621914916, 1.2721633525967888, 0.09148383753421385, false)
Quaternion{Float64}(0.3218637131935187, 0.41718708043753666, 1.2677495035291564, 0.09116642872804162, false)
Quaternion{Float64}(0.3191187911313047, 0.41623360609777327, 1.2648520824978169, 0.09095806932643001, false)
Quaternion{Float64}(0.3164892498533091, 0.4166775584788587, 1.2662011664869983, 0.09105508468238596, false)
Quaternion{Float64}(0.317054633113361, 0.41733360761104704, 1.2681947707969645, 0.09119844879708726, false)
Quaternion{Float64}(0.31863911536780903, 0.41731880617627404, 1.2681497921471816, 0.09119521429148635, false)
Quaternion{Float64}(0.31887176042403637, 0.41696678027062145, 1.2670800546408032, 0.09111828730562561, false)
Quaternion{Float64}(0.31811243187512667, 0.4168561076998873, 1.266743742460533, 0.09109410241710653, false)
Quaternion{Float64}(0.31773318001482903, 0.4170050654871516, 1.2671963958855939, 0.09112665363964648, false)
Quaternion{Float64}(0.31800748141371743, 0.4171138753649327, 1.2675270477082519, 0.09115043148041094, false)
Quaternion{Float64}(0.3183005734059548, 0.4170716351432334, 1.267398687980448, 0.09114120087298903, false)
Quaternion{Float64}(0.31825406326657096, 0.4169998423095536, 1.2671805236759373, 0.09112551223697474, false)
Quaternion{Float64}(0.3180833078791223, 0.4169980145490542, 1.2671749694711827, 0.09112511282288661, false)
Quaternion{Float64}(0.3180504013681607, 0.41703539792424593, 1.2672885701974799, 0.09113328208068446, false)
Quaternion{Float64}(0.318129705801897, 0.41704895514151064, 1.2673297679149127, 0.09113624469179937, false)
Quaternion{Float64}(0.3181738237438287, 0.4170337335864272, 1.2672835126021171, 0.09113291837878128, false)
Quaternion{Float64}(0.31814670852856086, 0.4170214332012489, 1.2672461341502566, 0.0911302304187718, false)
Quaternion{Float64}(0.3181142274023023, 0.41702534676476843, 1.2672580267002456, 0.09113108563607455, false)
Quaternion{Float64}(0.31811764001151954, 0.41703317508020965, 1.2672818154115442, 0.09113279633037741, false)
Quaternion{Float64}(0.3181359807845624, 0.4170337398944662, 1.267283531771007, 0.09113291975725488, false)
Quaternion{Float64}(0.3181403506683638, 0.41702978683721686, 1.267271519207339, 0.09113205590952593, false)
Quaternion{Float64}(0.31813211519911805, 0.4170281567121847, 1.2672665655779072, 0.09113169968402297, false)
Quaternion{Float64}(0.31812702900406814, 0.41702969996821443, 1.2672712552295222, 0.09113203692634768, false)
Quaternion{Float64}(0.3181296749814361, 0.4170310824455512, 1.267275456306304, 0.09113233903426882, false)
Quaternion{Float64}(0.3181332579789174, 0.41703073119894324, 1.2672743889369302, 0.09113226227758014, false)
Quaternion{Float64}(0.31813306412936865, 0.41702988121903445, 1.2672718060151238, 0.09113207653445336, false)
Quaternion{Float64}(0.31813110249399523, 0.41702978088837955, 1.267271501129992, 0.09113205460954742, false)
Quaternion{Float64}(0.3181305445031431, 0.41703019696768384, 1.2672727655131815, 0.0911321455338977, false)
Quaternion{Float64}(0.3181313948275616, 0.4170303901854323, 1.2672733526639255, 0.09113218775709422, false)
Quaternion{Float64}(0.3181319765021371, 0.417030235034959, 1.2672728811921452, 0.09113215385260572, false)
Quaternion{Float64}(0.31813172233439296, 0.4170300805240387, 1.2672724116638407, 0.09113212008787651, false)
Quaternion{Float64}(0.31813132888185675, 0.41703011060795825, 1.2672725030829564, 0.09113212666200986, false)
Quaternion{Float64}(0.31813133090804147, 0.41703020251629513, 1.2672727823743195, 0.09113214674641619, false)
Quaternion{Float64}(0.31813153983170894, 0.417030217544262, 1.2672728280413559, 0.09113215003042506, false)
Quaternion{Float64}(0.3181316091149064, 0.41703017396095676, 1.2672726956002613, 0.09113214050631831, false)
Quaternion{Float64}(0.3181315218699095, 0.4170301513303609, 1.2672726268303305, 0.09113213556093362, false)
Quaternion{Float64}(0.31813145582063, 0.41703016677663046, 1.2672726737685063, 0.0911321389363527, false)
Quaternion{Float64}(0.31813147975421563, 0.4170301839558242, 1.2672727259726981, 0.09113214269046165, false)
Quaternion{Float64}(0.318131522771595, 0.4170301815657699, 1.2672727187097932, 0.09113214216817148, false)
Quaternion{Float64}(0.3181315245905677, 0.41703017166853923, 1.2672726886340555, 0.09113214000536439, false)
Quaternion{Float64}(0.31813150243545035, 0.41703016960059547, 1.267272682349981, 0.09113213955346389, false)
Quaternion{Float64}(0.3181314940119317, 0.41703017414248317, 1.2672726961518845, 0.09113214054598666, false)
Quaternion{Float64}(0.31813150290125214, 0.41703017676647003, 1.2672727041256646, 0.0911321411193973, false)
Quaternion{Float64}(0.3181315103530424, 0.41703017524623537, 1.2672726995059704, 0.09113214078718575, false)
Quaternion{Float64}(0.31813150815763297, 0.4170301733455036, 1.2672726937300203, 0.09113214037182552, false)
Quaternion{Float64}(0.31813150347433916, 0.4170301735100363, 1.2672726942300028, 0.09113214040778027, false)
Quaternion{Float64}(0.31813150305918386, 0.41703017457143704, 1.267272697455391, 0.09113214063972445, false)
Quaternion{Float64}(0.3181315053980903, 0.417030174841785, 1.2672726982769253, 0.09113214069880264, false)
Quaternion{Float64}(0.31813150640545146, 0.4170301743710613, 1.2672726968464887, 0.09113214059593705, false)
Quaternion{Float64}(0.31813150550677766, 0.41703017406945775, 1.2672726959299747, 0.09113214053002866, false)
Quaternion{Float64}(0.3181315046709843, 0.41703017421703026, 1.2672726963784184, 0.09113214056227716, false)
Quaternion{Float64}(0.3181315048651666, 0.4170301744263544, 1.2672726970145136, 0.09113214060802004, false)
Quaternion{Float64}(0.3181315053729158, 0.41703017441873963, 1.2672726969913737, 0.091132140606356, false)
Quaternion{Float64}(0.3181315054411271, 0.41703017430538714, 1.2672726966469177, 0.09113214058158547, false)
Quaternion{Float64}(0.31813150519536304, 0.41703017427124556, 1.2672726965431682, 0.09113214057412464, false)
Quaternion{Float64}(0.31813150507649923, 0.41703017431974204, 1.2672726966905394, 0.09113214058472241, false)
Quaternion{Float64}(0.31813150516654626, 0.41703017435414336, 1.2672726967950783, 0.09113214059224001, false)
Quaternion{Float64}(0.3181315052597806, 0.41703017434006046, 1.2672726967522832, 0.09113214058916252, false)
Quaternion{Float64}(0.3181315052435185, 0.4170301743171106, 1.267272696682543, 0.09113214058414737, false)
Quaternion{Float64}(0.3181315051886964, 0.41703017431683576, 1.2672726966817078, 0.0911321405840873, false)
Quaternion{Float64}(0.318131505178842, 0.4170301743288898, 1.2672726967183376, 0.09113214058672142, false)
Quaternion{Float64}(0.3181315052045388, 0.4170301743330944, 1.267272696731115, 0.09113214058764026, false)
Quaternion{Float64}(0.31813150521840805, 0.4170301743281306, 1.267272696716031, 0.09113214058655554, false)
Quaternion{Float64}(0.3181315052094782, 0.4170301743242335, 1.2672726967041885, 0.09113214058570393, false)
Quaternion{Float64}(0.3181315051991303, 0.41703017432554834, 1.267272696708184, 0.09113214058599126, false)
Quaternion{Float64}(0.3181315052003719, 0.4170301743280538, 1.2672726967157975, 0.09113214058653876, false)
Quaternion{Float64}(0.31813150520626693, 0.4170301743282016, 1.2672726967162464, 0.09113214058657107, false)
Quaternion{Float64}(0.3181315052075948, 0.41703017432692535, 1.2672726967123682, 0.09113214058629218, false)
Quaternion{Float64}(0.31813150520492195, 0.41703017432641737, 1.2672726967108245, 0.09113214058618119, false)
Quaternion{Float64}(0.3181315052033192, 0.41703017432692185, 1.2672726967123575, 0.09113214058629142, false)
Quaternion{Float64}(0.3181315052041941, 0.4170301743273605, 1.2672726967136905, 0.09113214058638727, false)
Quaternion{Float64}(0.31813150520533695, 0.41703017432724127, 1.267272696713328, 0.09113214058636122, false)
Quaternion{Float64}(0.3181315052052588, 0.417030174326969, 1.2672726967125005, 0.09113214058630172, false)
Quaternion{Float64}(0.31813150520462746, 0.41703017432694034, 1.2672726967124135, 0.09113214058629546, false)
Quaternion{Float64}(0.31813150520445627, 0.4170301743270749, 1.2672726967128223, 0.09113214058632485, false)
Quaternion{Float64}(0.31813150520473266, 0.4170301743271354, 1.2672726967130061, 0.09113214058633808, false)
Quaternion{Float64}(0.3181315052049165, 0.41703017432708456, 1.2672726967128516, 0.09113214058632696, false)
Quaternion{Float64}(0.31813150520483213, 0.4170301743270355, 1.2672726967127024, 0.09113214058631623, false)