{"version":9,"randomSeed":"cab855d73f5ea5b4c25198d8ed9281b6","graph":{"viewport":{"xmin":-1.1750324042808826,"ymin":-2.0853435264977698,"xmax":21.403092595719134,"ymax":21.745590987618463},"showGrid":false},"expressions":{"list":[{"type":"text","id":"223","text":"inspired by \"Percolation: a Mathematical Phase Transition\" by Alves, Hruskova, Winstein, et al (2022) https://www.youtube.com/watch?v=a-767WnbaCQ"},{"type":"text","id":"231","text":"width and height"},{"type":"expression","id":"215","color":"#2d70b3","latex":"W=20","slider":{"hardMin":true,"hardMax":true,"min":"1","max":"100","step":"1"}},{"type":"expression","id":"216","color":"#2d70b3","latex":"H=20","slider":{"hardMin":true,"hardMax":true,"min":"1","max":"100","step":"1"}},{"type":"text","id":"233","text":"edge-probabilities along x- and y-direction"},{"type":"expression","id":"1","color":"#c74440","latex":"E_{x}=\\left[\\operatorname{random}\\left(\\right)\\operatorname{for}x_{1}=\\left[1...W\\right],y_{1}=\\left[1...H\\right]\\right]"},{"type":"expression","id":"217","color":"#388c46","latex":"E_{y}=\\left[\\operatorname{random}\\left(\\right)\\operatorname{for}x_{1}=\\left[1...W\\right],y_{1}=\\left[1...H\\right]\\right]"},{"type":"expression","id":"260","color":"#000000","latex":"\\left[\\operatorname{polygon}\\left(\\left(x_{1}-1,y_{1}\\right),\\left(x_{1},y_{1}\\right)\\right)\\operatorname{for}x_{1}=\\left[1...W\\right],y_{1}=\\left[1...H\\right]\\right]","fill":false,"fillOpacity":"","lineOpacity":"\\operatorname{ceil}\\left(p-E_{x}\\right)"},{"type":"expression","id":"261","color":"#000000","latex":"\\left[\\operatorname{polygon}\\left(\\left(x_{1},y_{1}-1\\right),\\left(x_{1},y_{1}\\right)\\right)\\operatorname{for}x_{1}=\\left[1...W\\right],y_{1}=\\left[1...H\\right]\\right]","lineOpacity":"\\operatorname{ceil}\\left(p-E_{y}\\right)"},{"type":"text","id":"236","text":"groupings"},{"type":"expression","id":"239","color":"#c74440","latex":"I_{0}\\left(x,y\\right)=W\\left(y-1\\right)+x"},{"type":"expression","id":"241","color":"#388c46","latex":"I\\left(x,y\\right)=I_{0}\\left(\\left\\{x\\le0:W,x>W:1,x\\right\\},\\left\\{y\\le0:H,y>H:1,y\\right\\}\\right)"},{"type":"folder","id":"263","title":"don't open","collapsed":true},{"type":"expression","id":"224","folderId":"263","color":"#6042a6","latex":"G=\\left[1,385,385,385,385,388,388,388,9,10,11,394,394,394,400,400,18,18,19,20,21,385,385,385,385,110,110,388,110,110,110,394,394,34,271,400,37,119,119,60,385,385,43,44,45,110,110,110,49,110,110,52,394,394,271,56,119,119,59,60,385,63,63,64,86,66,110,110,110,110,110,92,92,92,271,119,119,119,160,160,160,160,83,86,86,86,166,89,89,110,110,92,93,271,271,119,119,119,160,160,101,102,103,125,125,166,166,166,166,110,271,271,271,271,271,116,119,119,119,160,144,144,144,144,125,166,166,166,169,271,271,271,271,271,271,271,137,179,179,160,163,144,144,144,166,166,166,148,169,271,271,271,271,271,271,271,157,179,179,160,163,163,163,166,166,166,167,168,169,271,271,271,271,271,271,271,177,179,179,220,220,400,400,400,185,186,245,245,271,271,271,271,271,271,271,271,271,198,219,220,400,400,400,400,245,245,245,245,245,271,271,271,271,271,235,235,257,238,219,220,260,242,400,245,245,288,245,228,271,271,271,232,271,271,235,257,257,238,260,260,241,242,400,400,245,288,288,248,271,271,271,252,271,271,256,256,257,297,260,260,400,400,400,400,288,288,288,310,310,310,271,272,274,274,275,296,297,297,279,400,400,400,400,400,288,306,288,288,289,310,310,292,313,294,400,296,297,400,400,400,400,400,400,385,385,306,310,310,310,310,311,333,313,314,400,316,400,400,400,320,321,400,323,385,385,385,388,328,391,391,391,333,333,334,400,400,400,400,400,400,400,400,385,385,385,388,388,391,391,391,391,394,394,354,355,400,400,400,400,400,400,385,385,385,385,388,388,388,391,391,391,394,394,394,400,400,400,400,400,400,400,385,385,384,385,388,388,388,389,391,391,394,394,394,400,400,400,400,400,400\\right]","labelSize":"medium"},{"type":"expression","id":"226","color":"#c74440","latex":"G\\to\\left[W\\left(y_{1}-1\\right)+x_{1}\\operatorname{for}x_{1}=\\left[1...W\\right],y_{1}=\\left[1...H\\right]\\right]"},{"type":"text","id":"253","text":"colouring by groups"},{"type":"expression","id":"227","color":"#2d70b3","latex":"K=\\operatorname{shuffle}\\left(\\left[\\operatorname{hsv}\\left(\\frac{360}{WH}\\cdot I\\left(x_{1},y_{1}\\right),1,1\\right)\\operatorname{for}x_{1}=\\left[1...W\\right],y_{1}=\\left[1...H\\right]\\right]\\right)","labelSize":"medium"},{"type":"expression","id":"243","color":"#000000","latex":"K_{R}=\\left[K\\left[G\\left[I\\left(x_{2},y_{2}\\right)\\right]\\right]\\operatorname{for}x_{2}=\\left[1...W\\right],y_{2}=\\left[1...H\\right]\\right]"},{"type":"expression","id":"242","color":"#6042a6","latex":"\\left[\\left(x_{1},y_{1}\\right)\\operatorname{for}x_{1}=\\left[1...W\\right],y_{1}=\\left[1...H\\right]\\right]","labelSize":"medium","colorLatex":"K_{R}","pointOpacity":"1","pointSize":"30"},{"type":"text","id":"255","text":"the process"},{"type":"expression","id":"229","color":"#6042a6","latex":"p=0.4","slider":{"hardMin":true,"hardMax":true,"min":"0","max":"1"}},{"type":"text","id":"259","text":"choose maximum of possible edge-changes (max is arbitrary, just to make sure we pick something rather than oscillating)"},{"type":"expression","id":"256","color":"#c74440","latex":"T_{x}\\left(x,y,o\\right)=\\left\\{E_{x}\\left[I\\left(x+o,y\\right)\\right]<p:G\\left[I\\left(x+\\left(2o-1\\right),y\\right)\\right],0\\right\\}"},{"type":"expression","id":"257","color":"#2d70b3","latex":"T_{y}\\left(x,y,o\\right)=\\left\\{E_{y}\\left[I\\left(x,y+o\\right)\\right]<p:G\\left[I\\left(x,y+\\left(2o-1\\right)\\right)\\right],0\\right\\}"},{"type":"expression","id":"237","color":"#6042a6","latex":"S_{a}=\\left(G\\to\\left[\\max\\left(T_{x}\\left(x_{2},y_{2},0\\right),T_{x}\\left(x_{2},y_{2},1\\right),T_{y}\\left(x_{2},y_{2},0\\right),T_{y}\\left(x_{2},y_{2},1\\right),G\\left[I\\left(x_{2},y_{2}\\right)\\right]\\right)\\operatorname{for}x_{2}=\\left[1...W\\right],y_{2}=\\left[1...H\\right]\\right]\\right)","labelSize":"medium"}]}}