{"version":9,"randomSeed":"d76e4769046f6294671af95afdbffcef","graph":{"viewport":{"xmin":-0.5503885605380977,"ymin":-0.3912557961973192,"xmax":1.4473116906265844,"ymax":1.4173011339091106}},"expressions":{"list":[{"type":"text","id":"8","text":"decreasing radius wrt element index"},{"type":"expression","id":"2","color":"#2d70b3","latex":"r\\left(x\\right)=\\frac{0.2}{\\sqrt{x}}","hidden":true},{"type":"folder","id":"30","title":"circle centers","hidden":true,"collapsed":true},{"type":"expression","id":"3","folderId":"30","color":"#388c46","latex":"L=\\left[\\left(0.99,0.99\\right),\\left(0.028,0.987\\right),\\left(0.02,0.035\\right),\\left(0.964,0.046\\right),\\left(0.6772332682972003,0.09133996309892645\\right),\\left(0.0032122253589412786,0.3442452273179849\\right),\\left(0.22862230125880323,0.2786117947879788\\right),\\left(0.8350904841660857,0.4279075924126726\\right),\\left(0.980921501152967,0.6010300966397947\\right),\\left(0.5740314240369575,0.7022274744071306\\right),\\left(0.30956580642676124,0.6574327872403333\\right),\\left(0.5042547718216392,0.9698779284170406\\right),\\left(0.8077502024389666,0.5782675759589267\\right),\\left(0.18967112219482096,0.6632729640862878\\right),\\left(0.09652482923537375,0.6145232057565367\\right),\\left(0.9900107606901231,0.45907843187441144\\right),\\left(0.7630753324907252,0.7190161603239966\\right),\\left(0.6157717239706084,0.448464512169803\\right),\\left(0.2842085151612187,0.4038159862886732\\right),\\left(0.33822098688438507,0.20016963469383642\\right),\\left(0.8198485846860979,0.28942099265305476\\right),\\left(0.482142792407407,0.4587304396845808\\right),\\left(0.9708303992769701,0.36296622879646767\\right),\\left(0.23423064481367295,0.8301141333817061\\right),\\left(0.5164094943407402,0.26604350343526095\\right),\\left(0.42143873004517085,0.8691932977186305\\right),\\left(0.16226306140919,0.1309131597264137\\right),\\left(0.14958983182548924,0.37213609453762453\\right),\\left(0.5488135697196495,0.8771767801455936\\right),\\left(0.21976381086582963,0.9831901963376787\\right),\\left(0.1244926878201087,0.4862955864714269\\right),\\left(0.5546028539721807,0.06339573351320404\\right),\\left(0.9001724784430662,0.6905708962277579\\right),\\left(0.3824900071551016,0.09200828083203694\\right),\\left(0.7607927469333291,0.8757677045382933\\right),\\left(0.6562683807635559,0.6016807674752752\\right),\\left(0.06338191864156306,0.22407786611802638\\right),\\left(0.7495686184150259,0.32886998040202364\\right),\\left(0.4050214458092274,0.9433578886590408\\right),\\left(0.2282391671196895,0.5826667198601773\\right),\\left(0.03308862596799278,0.4734208675972882\\right),\\left(0.6597477192572495,0.2738675763233399\\right),\\left(0.49244866628786,0.18985334830193568\\right),\\left(0.4729036523875648,0.7947679178204762\\right),\\left(0.26782299190102166,0.05310180749204141\\right),\\left(0.9334802655956517,0.20172486404579948\\right),\\left(0.13660828704221728,0.8324983039747201\\right),\\left(0.40101985402472695,0.015627156079631388\\right),\\left(0.34260636387737353,0.4933031298762286\\right),\\left(0.5517596729715154,0.5571345481305322\\right),\\left(0.3005348458623106,0.8870105757751943\\right),\\left(0.8697396909398475,0.21909123309299539\\right),\\left(0.42048779747631404,0.7273032655751202\\right),\\left(0.7219267275353501,0.5104923410271306\\right),\\left(0.8456847621169002,0.1201527401680994\\right),\\left(0.14204734330399083,0.2223406015748045\\right),\\left(0.6374882839772341,0.5211114488492812\\right),\\left(0.3098676725792806,0.9726225307435364\\right),\\left(0.31333065815814964,0.5633115770218172\\right),\\left(0.4515181931674528,0.5988395713141501\\right),\\left(0.8061194034196735,0.7808796922838063\\right),\\left(0.6486568895415451,0.8310620213381981\\right),\\left(0.7184223205729886,0.961451059082779\\right),\\left(0.42884820559150627,0.3289074531506686\\right),\\left(0.21941323182958516,0.7368956098544847\\right),\\left(0.7152432089367879,0.2527973800764557\\right),\\left(0.24526085573789846,0.5265213601892745\\right),\\left(0.12004926598226406,0.3090813640778154\\right),\\left(0.9640157977527,0.2551502301513865\\right),\\left(0.39999370947138624,0.5613732330218686\\right),\\left(0.010140955061335721,0.7111330476441076\\right),\\left(0.8056259780831457,0.08706187402737775\\right),\\left(0.07842291956885261,0.16722379498766549\\right),\\left(0.8182960903082458,0.840595201999284\\right),\\left(0.2240551068789275,0.4447841905180413\\right),\\left(0.08269990379294379,0.8085549999728248\\right),\\left(0.6691645607365091,0.7501120526893922\\right),\\left(0.9026084286516866,0.34064346130659395\\right),\\left(0.12752049952209477,0.7232331657147737\\right),\\left(0.6787135832296255,0.4041376517727666\\right),\\left(0.1728807936158161,0.7832532400431147\\right),\\left(0.6457496703177633,0.881051988394684\\right),\\left(0.3003540848852496,0.7440227210404767\\right),\\left(0.5648008417121063,0.3144931919152668\\right),\\left(0.40508422165266433,0.24705889533207703\\right),\\left(0.4940774728118512,0.6694683288188038\\right),\\left(0.39454658816126664,0.6280238327487948\\right),\\left(0.5534894841399376,0.15519566843179755\\right),\\left(0.9919984910118413,0.16795346072887296\\right),\\left(0.5983397937475993,0.3695305953024297\\right),\\left(0.550111197203033,0.7917020746496416\\right),\\left(0.4845528572028559,0.006220149849355261\\right),\\left(0.5622691178226789,0.39767603295745957\\right),\\left(0.46362353903213993,0.05699181158057043\\right),\\left(0.6126458897825916,0.22534856268609027\\right),\\left(0.6617482785220865,0.9293620058537855\\right),\\left(0.25593523414887276,0.15020262446056298\\right),\\left(0.8248827818148851,0.6855418439107641\\right),\\left(0.77319889625102,0.8167735857406243\\right),\\left(0.44895098850614523,0.685469387165717\\right),\\left(0.08176912311062912,0.71312750417662\\right),\\left(0.7589837405248638,0.6423588603317925\\right),\\left(0.7258849913944236,0.7843569262534066\\right),\\left(0.15873972480921528,0.8848707361894945\\right),\\left(0.9234059804448821,0.5331814416319177\\right),\\left(0.884990591313508,0.7600757455611751\\right),\\left(0.1912325394206026,0.1874422954712721\\right),\\left(0.4758963500380934,0.11405825870622366\\right),\\left(0.5093070295281509,0.3425909948445103\\right),\\left(0.357821676968476,0.8894921117161604\\right),\\left(0.5897819396462916,0.010798139549478059\\right),\\left(0.024734067744483945,0.615639426471171\\right),\\left(0.7120768244683205,0.37079727523254213\\right),\\left(0.20907585301820442,0.04502367716864364\\right),\\left(0.7953018204864716,0.19598973048880075\\right),\\left(0.3766779674311348,0.2801394100209992\\right),\\left(0.5309430400982722,0.6123438039339546\\right),\\left(0.5774516859371402,0.9271994355940231\\right),\\left(0.03555768160607098,0.8198070456386306\\right),\\left(0.8075233215722336,0.0159406874691278\\right),\\left(0.6180118002540876,0.7773341353538334\\right),\\left(0.6382602894270782,0.3831165998599072\\right),\\left(0.1628510578074699,0.05445484644315357\\right),\\left(0.9918716227589648,0.7555811270326357\\right),\\left(0.7157310565756233,0.6531313302444094\\right),\\left(0.1807090935128547,0.01963623046816454\\right),\\left(0.9922423527305491,0.21978999386785836\\right),\\left(0.07022557891835579,0.5327800194503504\\right),\\left(0.39941870863048823,0.18810627059746066\\right),\\left(0.7673576539804721,0.030662203707035762\\right),\\left(0.6678236017956573,0.7903619279539306\\right),\\left(0.32585628854044424,0.29523689917349305\\right),\\left(0.36089791461131215,0.7604159764603952\\right),\\left(0.8769105077838335,0.16844302858347726\\right),\\left(0.5850060642242426,0.2774810061353743\\right),\\left(0.9015213833947302,0.6381156692910949\\right),\\left(0.7020123973908359,0.4680795164288223\\right),\\left(0.40401805012604186,0.4634347127823646\\right),\\left(0.32842219287500896,0.3335554824113346\\right),\\left(0.231469508322366,0.0056211729639151775\\right),\\left(0.7566143262571674,0.16208798200830576\\right),\\left(0.2806946809165004,0.782750693354698\\right),\\left(0.7674994932760443,0.9286232284610525\\right),\\left(0.8816021863957105,0.5613203489356213\\right),\\left(0.37057735159492466,0.7990088955094291\\right),\\left(0.06905480836772271,0.44134704264518454\\right),\\left(0.4630809974559985,0.28573264386523445\\right),\\left(0.171895700009967,0.559208543476142\\right),\\left(0.29226039850847607,0.4756723354833079\\right),\\left(0.35216774062592904,0.4120043057303686\\right),\\left(0.6782589096157032,0.552057940452303\\right),\\left(0.5167002819250935,0.7734886852825562\\right),\\left(0.9576403297370465,0.7588624170057084\\right),\\left(0.34530196396856483,0.9317341871268466\\right),\\left(0.8512768348305403,0.7163082174554973\\right),\\left(0.9866671837575306,0.297783387672496\\right),\\left(0.759700296751601,0.48073145386948146\\right),\\left(0.6648151761302895,0.2269630637826201\\right),\\left(0.4583913254176555,0.545542299598298\\right),\\left(0.7032196400875816,0.8787313136106856\\right),\\left(0.3734725208159614,0.3201278392770772\\right),\\left(0.4419321659061495,0.198969584291404\\right),\\left(0.3052658667199112,0.12718387174022106\\right),\\left(0.17875106753801318,0.7338942840095883\\right),\\left(0.3186016567796095,0.7987431551595343\\right),\\left(0.6306851009972805,0.9494833166143358\\right),\\left(0.6037507637964264,0.1839289086987359\\right),\\left(0.43811929234786884,0.12168397655522245\\right),\\left(0.2868324295533594,0.9369613406903551\\right),\\left(0.3169415616737191,0.05220041890339833\\right),\\left(0.45243004182072244,0.5143506057649178\\right),\\left(0.502961321587009,0.5450782543321537\\right),\\left(0.6104312758791305,0.5686573272095502\\right),\\left(0.521075111098138,0.5181571605922481\\right),\\left(0.023580710308976016,0.6618695844439575\\right),\\left(0.38749681756984433,0.4232956888311292\\right),\\left(0.7389873805347276,0.21751568086391748\\right),\\left(0.18345961439237168,0.5013179513990895\\right),\\left(0.6863964641187474,0.7007007200985175\\right),\\left(0.7724338507693478,0.9897159285073234\\right),\\left(0.60231236190516,0.9639175672417563\\right),\\left(0.7707845525737043,0.2575976792185233\\right),\\left(0.33000159810016116,0.8378989740283457\\right),\\left(0.4452627474086104,0.02188979756320819\\right),\\left(0.4349352911956489,0.37823627953940164\\right),\\left(0.4259392406057986,0.1591222581607319\\right),\\left(0.7444423309978128,0.4076499417063898\\right),\\left(0.8709747541939642,0.3184423120337849\\right),\\left(0.20067882400919812,0.08125842430069086\\right),\\left(0.5890289234082857,0.14687750406617273\\right),\\left(0.785328613677863,0.5088869249095563\\right),\\left(0.5790938631520536,0.598456727576999\\right),\\left(0.009270276593794424,0.5674952887632092\\right),\\left(0.2764814251599127,0.10056451368708941\\right),\\left(0.9201169670526972,0.2915952851378528\\right),\\left(0.24268079410144705,0.9047183508723694\\right),\\left(0.48026615738955014,0.387635276006135\\right),\\left(0.06252487586029465,0.758627222093446\\right),\\left(0.877406313834736,0.27961250442194563\\right),\\left(0.38356227366052476,0.6665011674168062\\right),\\left(0.36966518622911393,0.36008895289517184\\right),\\left(0.3511701144924255,0.9848671229415928\\right),\\left(0.3298361152173821,0.4512882464868714\\right),\\left(0.592381850819808,0.816154974275485\\right),\\left(0.9651784960351668,0.7053477683561871\\right),\\left(0.34725356275153796,0.126717597922416\\right),\\left(0.9050366858522855,0.7910133013062748\\right),\\left(0.8163421377466659,0.15341570544704453\\right),\\left(0.4076533894949729,0.7879128502374387\\right),\\left(0.2056173519759108,0.38891484419798805\\right),\\left(0.21344464621797354,0.8826651472419342\\right),\\left(0.15339582904355897,0.18299366597074684\\right),\\left(0.2315339746325802,0.08779115985161523\\right),\\left(0.2945894553394227,0.0004353683794161567\\right),\\left(0.7347493684509615,0.8231051712702703\\right),\\left(0.5001766666238935,0.5771126601923383\\right),\\left(0.5527670758970451,0.4782261364452951\\right),\\left(0.8436643710919958,0.019974795313162486\\right),\\left(0.8479516594811468,0.06423714316607687\\right),\\left(0.921806146135961,0.7652551056289804\\right),\\left(0.3450123003930933,0.7289240183742681\\right),\\left(0.5665445398124725,0.24735832461958396\\right),\\left(0.4773385322319875,0.8484405654880932\\right),\\left(0.42806036008628034,0.9893495091435186\\right),\\left(0.6161944151527822,0.908651404680493\\right),\\left(0.46357791086710964,0.35153764461191217\\right),\\left(0.42309809939418186,0.6568518123529934\\right),\\left(0.020842876663148213,0.5383904975161039\\right),\\left(0.9064614196529003,0.24241505394246043\\right),\\left(0.21365030218222925,0.146785558186725\\right),\\left(0.3269430075368943,0.09558464505948694\\right),\\left(0.5395906338661481,0.45044064882936274\\right),\\left(0.3617165884428921,0.4493418539467934\\right),\\left(0.7413783595667509,0.6127401573611354\\right),\\left(0.6190128413323156,0.3083466037580028\\right),\\left(0.13885213401996932,0.2665140495044541\\right),\\left(0.8726713850776965,0.6261182632485338\\right),\\left(0.35669518869630656,0.856315392252023\\right),\\left(0.7333462930387087,0.5676242575458302\\right),\\left(0.3298159429202763,0.003485704535143408\\right),\\left(0.39963406608371754,0.9879888745006274\\right),\\left(0.18819802769399618,0.47115252974602573\\right),\\left(0.6624324327613491,0.318642069770691\\right),\\left(0.5177590591732742,0.3923212022766287\\right),\\left(0.01753803437997692,0.23291328339369133\\right),\\left(0.9199463687999883,0.43069779834003497\\right),\\left(0.27317983067546936,0.19648298968020705\\right),\\left(0.12654874046132691,0.16783884346556233\\right),\\left(0.8025471429634287,0.34942194859952624\\right),\\left(0.2318016341038064,0.4840560851707616\\right),\\left(0.6488633287101515,0.34215980995913875\\right),\\left(0.3854378068395178,0.49893204367647637\\right),\\left(0.8604944429824387,0.7914955175558702\\right),\\left(0.8265903488271378,0.18248743456305472\\right),\\left(0.40913819054842704,0.2894740796820042\\right),\\left(0.3305515555326721,0.3672044213143931\\right),\\left(0.6538813470525894,0.19444704045086525\\right),\\left(0.7051006640767624,0.7529660495307224\\right),\\left(0.5742648599470321,0.49676108962819865\\right),\\left(0.4742787381822995,0.7441362466730705\\right),\\left(0.6476126072182206,0.6629881127272307\\right),\\left(0.7958286196270207,0.12562954035075102\\right),\\left(0.4253852944742156,0.4189831718581105\\right),\\left(0.7136927292951804,0.29375737386053213\\right),\\left(0.30232806910671495,0.347500309711841\\right),\\left(0.5030900700057997,0.8332428822279965\\right),\\left(0.08827447291041834,0.7700192561935306\\right),\\left(0.477473415976035,0.8810703139634215\\right),\\left(0.5475623969139398,0.11726319277674968\\right),\\left(0.12246655149970687,0.5530560688433931\\right),\\left(0.2957277513108564,0.8293647499035383\\right),\\left(0.912794263553767,0.456675771433005\\right),\\left(0.014320317835306962,0.20803046545728998\\right),\\left(0.67077174041235,0.6464536735109513\\right),\\left(0.525318323905479,0.0018679533945926696\\right),\\left(0.9160226263230862,0.7361834436979138\\right),\\left(0.3603476773822787,0.5538062164804252\\right),\\left(0.5978853767885971,0.3227071839534502\\right),\\left(0.5938941402696601,0.6259368806604637\\right),\\left(0.08574269685002389,0.2640951535448226\\right),\\left(0.7191661090607359,0.8527224442089248\\right),\\left(0.16139328323671653,0.43314404273977214\\right),\\left(0.49843725427357644,0.07875533051253447\\right),\\left(0.5099157014396792,0.12246989255057006\\right),\\left(0.007597707858959746,0.5146357127479256\\right),\\left(0.12957888644956594,0.7871907041133883\\right),\\left(0.13199387840525956,0.4337104866314805\\right),\\left(0.01984547246579471,0.765730894449783\\right),\\left(0.012436133522344628,0.17483702362259468\\right),\\left(0.6547309050371305,0.988161769704576\\right),\\left(0.679406607556253,0.9838536652515025\\right),\\left(0.24117300901939276,0.11398105351494858\\right),\\left(0.6987406702507437,0.21118917858953734\\right),\\left(0.4613759287808479,0.6452909456331105\\right),\\left(0.6942930960756762,0.8374375563979948\\right),\\left(0.0029998207996819737,0.6422604651777901\\right),\\left(0.2628910557038958,0.4620115426270778\\right),\\left(0.7947799566916124,0.6571578474310905\\right),\\left(0.0020866324387084356,0.8001505944455762\\right),\\left(0.8523945962546011,0.8258449043958793\\right)\\right]"},{"type":"text","id":"18","text":"are the circle with the given centre and the currently-added radius touching the circle at index i?"},{"type":"expression","id":"5","color":"#000000","latex":"T\\left(i,p\\right)=\\left\\{r\\left(i\\right)+r\\left(\\operatorname{length}\\left(L\\right)+1\\right)-\\operatorname{distance}\\left(L\\left[i\\right],p\\right)>0:1,0\\right\\}"},{"type":"text","id":"20","text":"is a circle centred at the given point and with the currently-added radius touching any established circles?"},{"type":"expression","id":"6","color":"#c74440","latex":"T_{a}\\left(p\\right)=\\left\\{\\sum_{k=1}^{\\operatorname{length}\\left(L\\right)}T\\left(k,p\\right)>0:1,0\\right\\}"},{"type":"folder","id":"33","title":"current point","collapsed":true},{"type":"expression","id":"21","folderId":"33","color":"#6042a6","latex":"c=\\left(0.4810036223673104,0.10681214736229161\\right)"},{"type":"expression","id":"23","folderId":"33","color":"#c74440","latex":"T_{a}\\left(c\\right)"},{"type":"expression","id":"4","folderId":"33","color":"#6042a6","latex":"r\\left(\\operatorname{length}\\left(L\\right)+1\\right)"},{"type":"expression","id":"22","color":"#000000","latex":"\\operatorname{distance}\\left(\\left(x,y\\right),c\\right)=r\\left(\\operatorname{length}\\left(L\\right)+1\\right)"},{"type":"expression","id":"24","color":"#2d70b3","latex":"A=\\left\\{\\max\\left(\\left|c.x-0.5\\right|,\\left|c.y-0.5\\right|\\right)\\le0.5:\\left\\{T_{a}\\left(c\\right)=0:L\\to\\operatorname{join}\\left(L,c\\right),L\\to L\\right\\},L\\to L\\right\\}"},{"type":"expression","id":"28","color":"#2d70b3","latex":"S=\\left(c\\to\\left(\\operatorname{random}\\left(\\right),\\operatorname{random}\\left(\\right)\\right)\\right)"},{"type":"expression","id":"25","color":"#388c46","latex":"\\operatorname{distance}\\left(L\\left[K\\right],\\left(x,y\\right)\\right)=r\\left(K\\right)"},{"type":"expression","id":"26","color":"#6042a6","latex":"K=\\left[1...\\operatorname{length}\\left(L\\right)\\right]"}],"ticker":{"handlerLatex":"A,S","minStepLatex":"100","open":true}}}