{"version":9,"randomSeed":"cf11e7d217fe692d991db2d469d419f3","graph":{"viewport":{"xmin":-1.4130043643650756,"ymin":-0.9884521829720418,"xmax":1.4611094131415856,"ymax":0.9820491695441984}},"expressions":{"list":[{"type":"expression","id":"1","color":"#c74440","latex":"n=8","slider":{"hardMin":true,"hardMax":true,"min":"1","step":"1"}},{"type":"text","id":"34","text":"described in and found through Terry R. McConnell's 2013 paper https://arxiv.org/abs/1303.6820"},{"type":"text","id":"36","text":"\"DeBruijn Strings, Double Helices, and the Ehrenfeucht-Mycielski Mechanism\""},{"type":"folder","id":"42","title":"solution","collapsed":true},{"type":"expression","id":"2","folderId":"42","color":"#2d70b3","latex":"L=\\left[0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,1,1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,1,1,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,1,1,1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0,1,1,0,0,0,0,1,0,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0\\right]"},{"type":"folder","id":"55","title":"circle display","collapsed":true},{"type":"expression","id":"48","folderId":"55","color":"#c74440","latex":"r\\le\\left(0\\cdot\\left[1...16\\right]+1\\right)\\cdot L\\left[\\operatorname{floor}\\left(\\frac{2^{n}\\theta}{2\\pi}\\right)\\right]","lines":false},{"type":"expression","id":"49","folderId":"55","color":"#388c46","latex":"r\\le\\left(0\\cdot\\left[1...16\\right]+1\\right)\\cdot\\left(1-L\\left[\\operatorname{floor}\\left(\\frac{2^{n}\\theta}{2\\pi}\\right)\\right]\\right)","lines":false},{"type":"text","id":"68","folderId":"55","text":"that +0x^3+0y^3 exists because of a bug in Desmos"},{"type":"expression","id":"50","folderId":"55","color":"#000000","latex":"y\\cos\\left(a\\right)=x\\sin\\left(a\\right)+0x^{3}+0y^{3}\\left\\{x^{2}+y^{2}\\le1\\right\\}"},{"type":"expression","id":"56","folderId":"55","color":"#2d70b3","latex":"a=\\pi\\frac{\\left[1...2^{n-1}\\right]}{2^{n-1}}"},{"type":"folder","id":"47","title":"linear display","hidden":true,"collapsed":true},{"type":"expression","id":"43","folderId":"47","color":"#c74440","latex":"\\left|y\\right|\\le L\\left[\\operatorname{round}\\left(x\\right)\\right]","lines":false,"fillOpacity":"1"},{"type":"expression","id":"44","folderId":"47","color":"#388c46","latex":"\\left|y\\right|\\le1-L\\left[\\operatorname{round}\\left(x\\right)\\right]","lines":false,"fillOpacity":"1"},{"type":"expression","id":"45","folderId":"47","color":"#000000","latex":"x=\\left[1...\\left(\\operatorname{length}\\left(L\\right)+1\\right)\\right]-\\frac{1}{2}\\left\\{-1\\le y\\le1\\right\\}"},{"type":"text","id":"60","text":"reset solution"},{"type":"expression","id":"31","color":"#000000","latex":"R=\\left(L\\to\\operatorname{join}\\left(0\\cdot\\left[1...n\\right],0\\cdot\\left[1...n\\right]+1\\right)\\right)"},{"type":"text","id":"16","text":"convert binary vector (little-endian) to number"},{"type":"expression","id":"4","color":"#6042a6","latex":"C_{bi}\\left(v\\right)=\\sum_{k=1}^{\\operatorname{length}\\left(v\\right)}v\\left[k\\right]2^{\\left(k-1\\right)}"},{"type":"folder","id":"25","title":"check for existing matches","collapsed":true},{"type":"text","id":"18","folderId":"25","text":"n-bit values encountered in v"},{"type":"expression","id":"9","folderId":"25","color":"#6042a6","latex":"S_{e}\\left(v\\right)=\\left[C_{bi}\\left(v\\left[K...\\left(K+n-1\\right)\\right]\\right)\\operatorname{for}K=\\left[1...\\left(\\operatorname{length}\\left(v\\right)-n+1\\right)\\right]\\right]"},{"type":"text","id":"62","folderId":"25","text":"n-bit values encountered in the solution so far"},{"type":"expression","id":"19","folderId":"25","color":"#c74440","latex":"S_{eLc}=S_{e}\\left(L\\right)"},{"type":"text","id":"64","folderId":"25","text":"same, but with the last value removed"},{"type":"expression","id":"21","folderId":"25","color":"#388c46","latex":"S_{eLt}=S_{eLc}\\left[1...\\left(\\operatorname{length}\\left(S_{eLc}\\right)-1\\right)\\right]"},{"type":"text","id":"66","folderId":"25","text":"duplicates of the last value in the preceding part of the solution"},{"type":"expression","id":"20","folderId":"25","color":"#2d70b3","latex":"S_{em}=S_{eLt}\\left[S_{eLt}=S_{eLc}\\left[\\operatorname{length}\\left(S_{eLc}\\right)\\right]\\right]"},{"type":"text","id":"28","text":"computation step: append a 1 if no duplicates, or correct the final element to a 0"},{"type":"expression","id":"29","color":"#388c46","latex":"A=\\left\\{\\operatorname{length}\\left(S_{em}\\right)=0:\\left(L\\to\\operatorname{join}\\left(L,1\\right)\\right),\\left(L\\to\\operatorname{join}\\left(L\\left[1...\\left(\\operatorname{length}\\left(L\\right)-1\\right)\\right],0\\right)\\right)\\right\\}"}],"ticker":{"handlerLatex":"A","minStepLatex":"100","open":true}}}