{"version":9,"randomSeed":"7caba758b9db29f5c7b8e37a54e1ef7d","graph":{"viewport":{"xmin":-19.999999999999993,"ymin":-20,"xmax":20.000000000000007,"ymax":20},"showGrid":false,"showXAxis":false,"showYAxis":false},"expressions":{"list":[{"type":"expression","id":"1","color":"#c74440","latex":"N=8","slider":{"hardMin":true,"hardMax":true,"min":"1","max":"16","step":"1"}},{"type":"expression","id":"2","color":"#2d70b3","latex":"B\\left(n,i\\right)=\\operatorname{floor}\\left(\\operatorname{mod}\\left(\\frac{n}{2^{i}},2\\right)\\right)"},{"type":"expression","id":"3","color":"#388c46","latex":"F\\left(n,i\\right)=\\left\\{B\\left(n,i\\right)=1:n-2^{i},n+2^{i}\\right\\}","labelSize":"medium"},{"type":"folder","id":"27","title":"sequence","collapsed":true},{"type":"expression","id":"4","folderId":"27","color":"#6042a6","latex":"G=\\left[0,1,3,2,6,7,5,4,12,13,15,14,10,11,9,8,24,25,27,26,30,31,29,28,20,21,23,22,18,19,17,16,48,49,51,50,54,55,53,52,60,61,63,62,58,59,57,56,40,41,43,42,46,47,45,44,36,37,39,38,34,35,33,32,96,97,99,98,102,103,101,100,108,109,111,110,106,107,105,104,120,121,123,122,126,127,125,124,116,117,119,118,114,115,113,112,80,81,83,82,86,87,85,84,92,93,95,94,90,91,89,88,72,73,75,74,78,79,77,76,68,69,71,70,66,67,65,64,192,193,195,194,198,199,197,196,204,205,207,206,202,203,201,200,216,217,219,218,222,223,221,220,212,213,215,214,210,211,209,208,240,241,243,242,246,247,245,244,252,253,255,254,250,251,249,248,232,233,235,234,238,239,237,236,228,229,231,230,226,227,225,224,160,161,163,162,166,167,165,164,172,173,175,174,170,171,169,168,184,185,187,186,190,191,189,188,180,181,183,182,178,179,177,176,144,145,147,146,150,151,149,148,156,157,159,158,154,155,153,152,136,137,139,138,142,143,141,140,132,133,135,134,130,131,129,128,0\\right]"},{"type":"folder","id":"17","title":"linear display","hidden":true,"collapsed":true},{"type":"expression","id":"5","folderId":"17","color":"#388c46","latex":"B\\left(G\\left[\\operatorname{ceil}\\left(y\\right)\\right],\\operatorname{floor}\\left(x\\right)\\right)\\le0.5\\left\\{0\\le x\\le N\\right\\}\\left\\{0\\le y\\le\\operatorname{length}\\left(G\\right)\\right\\}","lines":false,"fillOpacity":"1"},{"type":"expression","id":"7","folderId":"17","color":"#c74440","latex":"B\\left(G\\left[\\operatorname{ceil}\\left(y\\right)\\right],\\operatorname{floor}\\left(x\\right)\\right)\\ge0.5\\left\\{0\\le x\\le N\\right\\}\\left\\{0\\le y\\le\\operatorname{length}\\left(G\\right)\\right\\}","lines":false,"fillOpacity":"1"},{"type":"folder","id":"19","title":"circular display","collapsed":true},{"type":"text","id":"21","folderId":"19","text":"see https://www.desmos.com/calculator/euej3m66wx"},{"type":"expression","id":"23","folderId":"19","color":"#2d70b3","latex":"M=\\operatorname{distance}\\left(\\left(0,0\\right),\\left(x,y\\right)\\right)","labelSize":"medium"},{"type":"expression","id":"24","folderId":"19","color":"#388c46","latex":"A=2^{N}\\cdot\\frac{\\arctan\\left(y,x\\right)+\\pi}{2\\pi}+1"},{"type":"expression","id":"30","folderId":"19","color":"#388c46","latex":"C\\left(\\theta\\right)=\\left(\\cos\\theta,\\sin\\theta\\right)"},{"type":"expression","id":"31","folderId":"19","color":"#6042a6","latex":"O=\\operatorname{join}\\left(\\left[B\\left(G\\left[\\operatorname{floor}\\left(\\frac{k}{N}\\right)+1\\right],\\operatorname{mod}\\left(k,N\\right)\\right)\\operatorname{for}k=\\left[0...\\left(N\\cdot\\left(\\operatorname{length}\\left(G\\right)-1\\right)\\right)\\right]\\right],\\left[0.5\\operatorname{for}k=\\left[\\left(N\\cdot\\left(\\operatorname{length}\\left(G\\right)-1\\right)+1\\right)...N\\cdot2^{N}-1\\right]\\right]\\right)"},{"type":"expression","id":"28","folderId":"19","color":"#c74440","latex":"\\left[\\operatorname{polygon}\\left(\\left(N+\\operatorname{mod}\\left(k,N\\right)\\right)C\\left(\\frac{2\\pi}{2^{N}}\\operatorname{floor}\\left(\\frac{k}{N}\\right)\\right),\\left(N+\\operatorname{mod}\\left(k,N\\right)+1\\right)C\\left(\\frac{2\\pi}{2^{N}}\\operatorname{floor}\\left(\\frac{k}{N}\\right)\\right),\\left(N+\\operatorname{mod}\\left(k,N\\right)+1\\right)C\\left(\\frac{2\\pi}{2^{N}}\\left(\\operatorname{floor}\\left(\\frac{k}{N}\\right)+1\\right)\\right),\\left(N+\\operatorname{mod}\\left(k,N\\right)\\right)C\\left(\\frac{2\\pi}{2^{N}}\\left(\\operatorname{floor}\\left(\\frac{k}{N}\\right)+1\\right)\\right)\\right)\\operatorname{for}k=\\left[0...N\\cdot2^{N}-1\\right]\\right]","lines":false,"fillOpacity":"O"},{"type":"expression","id":"39","folderId":"19","color":"#388c46","latex":"\\left[\\operatorname{polygon}\\left(\\left(N+\\operatorname{mod}\\left(k,N\\right)\\right)C\\left(\\frac{2\\pi}{2^{N}}\\operatorname{floor}\\left(\\frac{k}{N}\\right)\\right),\\left(N+\\operatorname{mod}\\left(k,N\\right)+1\\right)C\\left(\\frac{2\\pi}{2^{N}}\\operatorname{floor}\\left(\\frac{k}{N}\\right)\\right),\\left(N+\\operatorname{mod}\\left(k,N\\right)+1\\right)C\\left(\\frac{2\\pi}{2^{N}}\\left(\\operatorname{floor}\\left(\\frac{k}{N}\\right)+1\\right)\\right),\\left(N+\\operatorname{mod}\\left(k,N\\right)\\right)C\\left(\\frac{2\\pi}{2^{N}}\\left(\\operatorname{floor}\\left(\\frac{k}{N}\\right)+1\\right)\\right)\\right)\\operatorname{for}k=\\left[0...N\\cdot2^{N}-1\\right]\\right]","lines":false,"fillOpacity":"1-O"},{"type":"expression","id":"8","color":"#2d70b3","latex":"G\\to\\operatorname{join}\\left(G,F\\left(G\\left[\\operatorname{length}\\left(G\\right)\\right],I\\left(G\\left[\\operatorname{length}\\left(G\\right)\\right]\\right)\\right)\\right)"},{"type":"expression","id":"15","color":"#2d70b3","latex":"G\\to\\left[0\\right]"},{"type":"text","id":"13","text":"TODO: ugly and overcomplicated, plz simplify"},{"type":"expression","id":"9","color":"#fa7e19","latex":"I\\left(n\\right)=\\left\\{\\operatorname{mod}\\left(\\sum_{i=0}^{N-1}B\\left(n,i\\right),2\\right)=0:0,B\\left(n,0\\right)=1:1,B\\left(n,1\\right)=1:2,B\\left(n,2\\right)=1:3,B\\left(n,3\\right)=1:4,B\\left(n,4\\right)=1:5,B\\left(n,5\\right)=1:6,B\\left(n,6\\right)=1:7,B\\left(n,7\\right)=1:7\\right\\}","hidden":true},{"type":"expression","id":"14","color":"#fa7e19","latex":"I\\left(\\operatorname{floor}\\left(x\\right)\\right)","hidden":true,"labelSize":"medium"}],"ticker":{"handlerLatex":"G\\to\\operatorname{join}\\left(G,F\\left(G\\left[\\operatorname{length}\\left(G\\right)\\right],I\\left(G\\left[\\operatorname{length}\\left(G\\right)\\right]\\right)\\right)\\right)","minStepLatex":"10","open":true}}}