In this location the central dominant minibrot has period 418864. Computing the zero crossing of the corresponding polynomial locates the minibrot at
-1.76979700322139811591272513043899832799423369499068746040312321369139476279899734327685384106424938431439273576680330733704966546075580838901324891220246239218903287505782319765936273238087369689487534737359516124840715760630396132975573610932201163074628687245503337178276171115248596381484098549511985811224780956321700144001233548139295889127740464191577029223476957057942352608361586911947339765514426923055404845140828712983972948274581253682130400984935617578642192675431716605409501767773747890962982410145941148467865154044608549657935615408744476886410714406890349574710784014258749496483079037310546638701763780494020009322694833109833656402410119130478284600925109395602405485985011438094250629579927270304012249169584818855490091011034850066008814214293599691799941578041340907231850565831837098638971449938935994601792205438960554930723986381877122351711795882803085844823543736994077850454865580941408628641027809410360282931245336574301206947989732268717006195367435719086670011251760720899568816751908549316856858712898480478800635959347100781293499250828473881321840106718612921692041981341359850708691437845116651465935653020129685931665064112991181637664436069589912197864687625835231334856460972500730321507970263314589963166350417424706366261835720179449175566433458116106325171826646992999680483823690344872849669066814331960087408951512529176426834553498117497629197785569880574692522939972961522510960524534583072265551760614774450799723561044615076588827984931672903629230164610169826241538784865555145381338917258229559017138074679046545750565703569290153270887791912366870238890702486377674493961627842425415072641536223340784982438486048756109238181153075391103742999718461989487988255182749425809658290851105686957800331487046619356847741786931568734133797812990312933679468689355633257241932332586807751783991361005487951858068862626827875513314445086552403572026135269341415265563914895613317095945080129111249617399947471951570374601941026322586575889678534000148411715548247602090863178460885536238487047026969052782268862081294620522011538188275677933094565746782844741895263212598E+00
4.503808149118977453591027370762118116191847489651632102771075493630536031121753213019458488948070234821894347490919752
32128719902266967792409275276218671134664739202538733880630147980377066457243173553858784184258065626405478713476529943
75685863015511904074453632654407731289619946868720085884280405841386804671414034982833768121999000401733388984737998508
35523341852444210373993799979274072458522457971439601401283190488219977380751679864657632594486990141780409069050808535
33679083210095437351400022620788443700681865056074859184889623921225508741770547501475133877301147491846294015630493195
94413147950329230917914373568299313895801070552430312839787385413077643433921434686758800882730741386718858427487804801
73527152642383437688144097648231731279522222357988455250353865370120443546331395472996006556618614941953429666058354649
10451202485512530423175907298924572677884684325102852936015719933302605823099958630951988450410491580664701963842251461
35190645341340161891884063141465638742680614101092435645795624718302058131414609501281021540435472453888874524109018147
02121578711328524425442226752168664749086242203613749999027884515745350840633982861734634138141253642303937961493945458
38176191438823739844915158113285022936463789829746280707055929391192625872076997627990447836359937976951672647199177818
72517689037585583899463944250055017306480718807197254236743510423432718914191161718864625412816080818679138546319519759
89748541205329675986737013154577653006827691952880225127567357459621316524513472420563020300861878311519895655738526548
29737784116356975937395880502857287215780402078167418834602295096014173047038182390355477059048628119343002217338189674
84428900612407421285966391654470156922336601567981570299684787648714514350236588685564191491795576963451396365624203611
89623693814216660262167258794137460777065623334381376669587093792227710384619914833779522355034279775231366236846879929
65077410226071259699613708732240144706025226046260403350230398624904436384826525344982234790191805054228954439652523570
302168603714064304338213704267058855190821114715226120756650420403035424042014899248446596447E-03
2.0E-2105
There is another juncture at 1.7E-1851 .
Now a question for Kalle and other fractal champions: How much can you skip near the minibrot?
A program option suited best for your needs would allow you to click on a pixel where you want to use a minibrot deep down in the neighbourhood of that pixel, locate the minibrot, compute one or more fork locations in between and generate images of the fork locations for you so you can click again on other pixels to deviate from the central minibrot. And so on. Pretty straightforward to implement.