{"version":9,"randomSeed":"02e6824b6e275ab36a82bbd0ebd56741","graph":{"viewport":{"xmin":-4.850487885917673,"ymin":-2.6446090670174947,"xmax":31.820227539380483,"ymax":22.76539478204828},"showGrid":false},"expressions":{"list":[{"type":"folder","id":"49","title":"library of useful functions","collapsed":true},{"type":"text","id":"50","folderId":"49","text":"project, R^3 -> R^2"},{"type":"expression","id":"51","folderId":"49","color":"#2d70b3","latex":"P\\left(v\\right)=\\frac{\\left(v\\left[1\\right],v\\left[2\\right]\\right)}{v\\left[3\\right]}"},{"type":"text","id":"52","folderId":"49","text":"dot product, R^n -> R^n -> R"},{"type":"expression","id":"53","folderId":"49","color":"#c74440","latex":"D\\left(u,v\\right)=\\sum_{k=1}^{\\min\\left(\\operatorname{length}\\left(u\\right),\\operatorname{length}\\left(v\\right)\\right)}u\\left[k\\right]v\\left[k\\right]"},{"type":"text","id":"54","folderId":"49","text":"cross product, R^3 -> R^3"},{"type":"text","id":"56","folderId":"49","text":"normalise vector, R^n -> R^n"},{"type":"text","id":"58","folderId":"49","text":"insert element as replacement, R^n -> N -> {R, R^2} -> R^n"},{"type":"expression","id":"59","folderId":"49","color":"#2d70b3","latex":"I\\left(v,i,x\\right)=\\left\\{i=1:\\operatorname{join}\\left(x,v\\left[2...\\right]\\right),i=\\operatorname{length}\\left(v\\right):\\operatorname{join}\\left(v\\left[1...\\operatorname{length}\\left(v\\right)-1\\right],x\\right),\\operatorname{join}\\left(v\\left[1...i-1\\right],x,v\\left[i+1...\\right]\\right)\\right\\}"},{"type":"text","id":"60","folderId":"49","text":"rotate around each axis, R^3 -> R^3"},{"type":"expression","id":"61","folderId":"49","color":"#2d70b3","latex":"R_{x}\\left(v,\\theta\\right)=\\left[v\\left[1\\right],v\\left[2\\right]\\cos\\theta-v\\left[3\\right]\\sin\\theta,v\\left[2\\right]\\sin\\theta+v\\left[3\\right]\\cos\\theta\\right]"},{"type":"expression","id":"62","folderId":"49","color":"#388c46","latex":"R_{y}\\left(v,\\theta\\right)=\\left[v\\left[1\\right]\\cos\\theta-v\\left[3\\right]\\sin\\theta,v\\left[2\\right],v\\left[1\\right]\\sin\\theta+v\\left[3\\right]\\cos\\theta\\right]"},{"type":"expression","id":"63","folderId":"49","color":"#6042a6","latex":"R_{z}\\left(v,\\theta\\right)=\\left[v\\left[1\\right]\\cos\\theta-v\\left[2\\right]\\sin\\theta,v\\left[1\\right]\\sin\\theta+v\\left[2\\right]\\cos\\theta,v\\left[3\\right]\\right]"},{"type":"expression","id":"1","color":"#c74440","latex":"w=20","slider":{"hardMin":true,"hardMax":true,"min":"1","max":"100","step":"1"}},{"type":"expression","id":"22","color":"#2d70b3","latex":"h=20","slider":{"hardMin":true,"hardMax":true,"min":"1","max":"100","step":"1"}},{"type":"folder","id":"30","title":"data","collapsed":true},{"type":"expression","id":"27","folderId":"30","color":"#c74440","latex":"L=\\left[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0\\right]"},{"type":"expression","id":"28","color":"#2d70b3","latex":"R=\\left(L\\to\\left[1...\\left(wh\\right)\\right]\\cdot0\\right)"},{"type":"expression","id":"88","color":"#2d70b3","latex":"L\\to\\operatorname{join}\\left(L,\\left[1...\\left(wh-\\operatorname{length}\\left(L\\right)\\right)\\right]\\right)"},{"type":"folder","id":"74","title":"implementation"},{"type":"expression","id":"33","folderId":"74","color":"#000000","latex":"C\\left(v,i\\right)=I\\left(v,i,1-v\\left[i\\right]\\right)"},{"type":"expression","id":"31","folderId":"74","color":"#000000","latex":"\\left[\\left(x_{1},y_{1}\\right)\\operatorname{for}x_{1}=\\left[1...w\\right],y_{1}=\\left[1...h\\right]\\right]\\left\\{\\left[L\\left[w\\left(y_{1}-1\\right)+x_{1}\\right]\\operatorname{for}x_{1}=\\left[1...w\\right],y_{1}=\\left[1...h\\right]\\right]=0\\right\\}","dragMode":"NONE","pointOpacity":"0.2","pointSize":"20","clickableInfo":{"enabled":true,"latex":"L\\to C\\left(L,\\operatorname{index}\\right)"}},{"type":"expression","id":"32","folderId":"74","color":"#000000","latex":"\\left[\\left(x_{1},y_{1}\\right)\\operatorname{for}x_{1}=\\left[1...w\\right],y_{1}=\\left[1...h\\right]\\right]\\left\\{\\left[L\\left[w\\left(y_{1}-1\\right)+x_{1}\\right]\\operatorname{for}x_{1}=\\left[1...w\\right],y_{1}=\\left[1...h\\right]\\right]=1\\right\\}","dragMode":"NONE","pointOpacity":"1","pointSize":"20","clickableInfo":{"enabled":true,"latex":"L\\to C\\left(L,\\operatorname{index}\\right)"}},{"type":"text","id":"67","folderId":"74","text":"transform a cell given state and number of live neighbours"},{"type":"expression","id":"65","folderId":"74","color":"#2d70b3","latex":"T\\left(s,k\\right)=\\left\\{s=0:\\left\\{k=3:1,0\\right\\},s=1:\\left\\{2\\le k\\le3:1,0\\right\\}\\right\\}"},{"type":"text","id":"69","folderId":"74","text":"obtain count of live neighbours around index"},{"type":"expression","id":"70","folderId":"74","color":"#000000","latex":"N\\left(v,k\\right)=A\\left(v,k-w-1\\right)+A\\left(v,k-w\\right)+A\\left(v,k-w+1\\right)+A\\left(v,k-1\\right)+A\\left(v,k+1\\right)+A\\left(v,k+w-1\\right)+A\\left(v,k+w\\right)+A\\left(v,k+w+1\\right)"},{"type":"expression","id":"72","folderId":"74","color":"#2d70b3","latex":"A\\left(v,k\\right)=v\\left[\\operatorname{mod}\\left(k-1,\\operatorname{length}\\left(v\\right)\\right)+1\\right]"},{"type":"expression","id":"64","folderId":"74","color":"#c74440","latex":"S=\\left(L\\to\\left[T\\left(L\\left[i\\right],N\\left(L,i\\right)\\right)\\operatorname{for}i=\\left[1...\\left(wh\\right)\\right]\\right]\\right)"},{"type":"folder","id":"76","title":"presets (20x20)","collapsed":true},{"type":"text","id":"80","folderId":"76","text":"blank"},{"type":"expression","id":"81","folderId":"76","color":"#2d70b3","latex":"R"},{"type":"text","id":"83","folderId":"76","text":"lone glider"},{"type":"expression","id":"85","folderId":"76","color":"#000000","latex":"L\\to\\left[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0\\right]"},{"type":"text","id":"86","folderId":"76","text":"R-pentomino"},{"type":"expression","id":"87","folderId":"76","color":"#c74440","latex":"L\\to\\left[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0\\right]"}],"ticker":{"handlerLatex":"S","minStepLatex":"10","open":true}}}