{"version":9,"randomSeed":"027522d981741090eae18217c1e6feb0","graph":{"viewport":{"xmin":-2.4999999999999987,"ymin":-2.0215517241379333,"xmax":2.500000000000002,"ymax":2.0215517241379297},"showGrid":false,"showXAxis":false,"showYAxis":false},"expressions":{"list":[{"type":"text","id":"67","text":"see https://en.wikipedia.org/wiki/Julia_set"},{"type":"folder","id":"24","title":"utilities","collapsed":true},{"type":"text","id":"10","folderId":"24","text":"multiplication and division of complex numbers (as points)"},{"type":"expression","id":"2","folderId":"24","color":"#2d70b3","latex":"m\\left(w,z\\right)=\\left(w.x\\cdot z.x-w.y\\cdot z.y,w.x\\cdot z.y+w.y\\cdot z.x\\right)"},{"type":"text","id":"12","folderId":"24","text":"see https://en.wikipedia.org/wiki/Division_%28mathematics%29#Of_complex_numbers"},{"type":"expression","id":"5","folderId":"24","color":"#000000","latex":"d\\left(w,z\\right)=\\frac{\\left(w.x\\cdot z.x+w.y\\cdot z.y,w.y\\cdot z.x-w.x\\cdot z.y\\right)}{z.x^{2}+z.y^{2}}"},{"type":"folder","id":"20","title":"setup","collapsed":true},{"type":"expression","id":"61","folderId":"20","color":"#2d70b3","latex":"c=\\left(-0.4,0.6\\right)"},{"type":"text","id":"14","folderId":"20","text":"function to iterate: z -> z^2 + c"},{"type":"expression","id":"1","folderId":"20","color":"#c74440","latex":"f\\left(z\\right)=m\\left(z,z\\right)+c"},{"type":"text","id":"59","folderId":"20","text":"four iterations"},{"type":"expression","id":"60","folderId":"20","color":"#c74440","latex":"Q\\left(z\\right)=f\\left(f\\left(f\\left(f\\left(z\\right)\\right)\\right)\\right)"},{"type":"text","id":"63","text":"preview and detail"},{"type":"expression","id":"64","color":"#fa7e19","latex":"\\operatorname{distance}\\left(\\left(0,0\\right),Q\\left(\\left(x,y\\right)\\right)\\right)\\le2","lines":false,"fillOpacity":"1"},{"type":"expression","id":"65","color":"#c74440","latex":"\\operatorname{distance}\\left(\\left(0,0\\right),Q\\left(Q\\left(\\left(x,y\\right)\\right)\\right)\\right)\\le2","lines":false,"fillOpacity":"1"},{"type":"expression","id":"53","color":"#388c46","latex":"\\operatorname{distance}\\left(\\left(0,0\\right),Q\\left(Q\\left(Q\\left(\\left(x,y\\right)\\right)\\right)\\right)\\right)\\le2","lines":false,"fillOpacity":"1"},{"type":"expression","id":"68","color":"#000000","latex":"\\operatorname{distance}\\left(\\left(0,0\\right),Q\\left(Q\\left(Q\\left(Q\\left(\\left(x,y\\right)\\right)\\right)\\right)\\right)\\right)\\le2","lines":false,"fillOpacity":"1"}]}}