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2848 days ago by ajbolt

from collections import deque import time def createCirclesAround(n): return matrix([ [1, 0, 0, 0], [0, 0, 1, 0], [4*cos(pi/n)^2, 1, 4*cos(pi/n)^2, 4*cos(pi/n)], [-2*cos(pi/n), 0, -2*cos(pi/n), -1] ]) def changeHub(n): return matrix([ [0, 1, 0, 0], [0, 0, 1, 0], [1, 0, 0, 0], [0, 0, 0, 1] ]) def changePerspective(n) : return matrix([ [1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, -1] ]) def rotate(n, k) : return matrix([ [cos(k*2*pi/n), sin(k*2*pi/n)], [-sin(k*2*pi/n), cos(k*2*pi/n)] ]) def startingValues(n): return matrix([ [0, 0, 1/(1-sin(pi/n))], [cos(4*pi/n)*csc(pi/n), sin(4*pi/n)*csc(pi/n), csc(pi/n)], [cos(2*pi/n)*csc(pi/n), sin(2*pi/n)*csc(pi/n), csc(pi/n)], [-cos(3*pi/n)*csc(pi/n), -1-2*cos(2*pi/n), cot(pi/n)/(-1+sin(pi/n))] ]) def createCircles(n, maxDepth, maxCDepth, withC, colors): class CircleInfo: def __init__(self, S, depth, depthBeforeC, lastOne, initialC, isC, isFirstC, colorOrder): self.S = S self.lastOne = lastOne self.initialC = initialC self.depth = depth self.depthBeforeC = depthBeforeC self.isC = isC self.isFirstC = isFirstC self.colorOrder = colorOrder # precompute powers of A and B to reduce amount of matrix multiplication - cut time in half A = [] for x in range(0,n): A.append(N(createCirclesAround(n))^x) B = [] for x in range(0,3): B.append(N(changeHub(n))^x) C = N(changePerspective(n)) AB = A[1]*B[1] #A*B BC = B[1]*C #B*C BBC = B[2]*C #B^2*C startVals = N(startingValues(n)) stack = [] f = file(DATA + 'test.csv', 'w') curvature = (startVals)[0][2] xCoord = (startVals)[0][0]/curvature yCoord = (startVals)[0][1]/curvature circle = '%.30f' % xCoord + ',' + '%.30f' % yCoord + ',' + '%.30f' % curvature + ',' + str(colors[0]) + '\r\n' f.write(circle) stack.append(CircleInfo(startVals, 0, 0, False, True, False, True, deque(colors))) while (stack != []): pop = stack.pop() depth = pop.depth depthBeforeC = pop.depthBeforeC initialC = pop.initialC isC = pop.isC isFirstC = pop.isFirstC lastOne = pop.lastOne S = pop.S colorOrder = pop.colorOrder if (isC and isFirstC and depth > 0): depthBeforeC = depth depth = 1 isFirstC = False if (not isC and depth >= maxDepth): continue elif (isC and depth >= maxCDepth - depthBeforeC + 2): continue elif (isC and depth >= 4): continue if (depth == 0): lower = 0 upper = n elif (initialC): lower = 2 upper = n - 1 initialC = False elif (depth > 1 and lastOne): lower = 2 upper = n - 3 lastOne = False if (withC): Z = AB*S newColorOrder = deque(colorOrder) newColorOrder.rotate(-1) # B left = newColorOrder.pop() # right = newColorOrder.pop() # newColorOrder.append(left) # newColorOrder.append(right) # all A left = newColorOrder.pop() # right = newColorOrder.pop() # newColorOrder.append(left) # newColorOrder.append(right) # all C stack.append(CircleInfo(C*Z, depth, depthBeforeC, False, True, True, isFirstC, deque(newColorOrder))) newColorOrder.rotate(-1) # B stack.append(CircleInfo(BC*Z, depth, depthBeforeC, False, True, True, isFirstC, deque(newColorOrder))) newColorOrder.rotate(-1) # B stack.append(CircleInfo(BBC*Z, depth, depthBeforeC, False, True, True, isFirstC, deque(newColorOrder))) else: lower = 2 upper = n - 2 for x in range(lower, upper): Z = A[x]*S newColorOrder = deque(colorOrder) newNColorOrder = deque(colorOrder) color = colorOrder[2] if (depth == 0 or x != 0): left = colorOrder.pop() right = colorOrder.pop() colorOrder.append(left) colorOrder.append(right) curvature = (Z)[2][2] xCoord = (Z)[2][0]/curvature yCoord = (Z)[2][1]/curvature circle = '%.30f' % xCoord + ',' + '%.30f' % yCoord + ',' + '%.30f' % curvature + ',' + str(color) + '\r\n' f.write(circle) if (withC): left = newColorOrder.pop() # right = newColorOrder.pop() # newColorOrder.append(left) # newColorOrder.append(right) # all C stack.append(CircleInfo(C*Z, depth+1, depthBeforeC, False, True, True, isFirstC, deque(newColorOrder))) newColorOrder.rotate(-1) # B stack.append(CircleInfo(BC*Z, depth+1, depthBeforeC, False, True, True, isFirstC, deque(newColorOrder))) newColorOrder.rotate(-1) # B stack.append(CircleInfo(BBC*Z, depth+1, depthBeforeC, False, True, True, isFirstC, deque(newColorOrder))) newNColorOrder.rotate(-2) # B^2 stack.append(CircleInfo(B[2]*Z, depth+1, depthBeforeC, x == upper - 1, False, isC, isFirstC, deque(newNColorOrder))) if (withC and depth == maxDepth - 1): Z = A[upper]*S newColorOrder = deque(colorOrder) left = newColorOrder.pop() # right = newColorOrder.pop() # newColorOrder.append(left) # newColorOrder.append(right) # all C stack.append(CircleInfo(C*Z, depth+1, depthBeforeC, False, True, True, isFirstC, deque(newColorOrder))) newColorOrder.rotate(-1) # B stack.append(CircleInfo(BC*Z, depth+1, depthBeforeC, False, True, True, isFirstC, deque(newColorOrder))) newColorOrder.rotate(-1) # B stack.append(CircleInfo(BBC*Z, depth+1, depthBeforeC, False, True, True, isFirstC, deque(newColorOrder))) def addAllBranches(circles, n, colors): R = [] for x in range(0, n): R.append(N(rotate(n, x))) for i in range(1, len(circles)): #dont do with first one in circles for x in range (1, n): color = circles[i][3] if (x % 2 == 1): if (color == colors[2]): color = colors[1] elif (color == colors[1]): color = colors[2] newCircle = matrix([circles[i][0], circles[i][1]])*R[x] circles.append([newCircle[0][0], newCircle[0][1], circles[i][2], color]) def addNumsToPlot(n, circles, fontSize): k = 0 numList = Graphics() for c in circles: numList += text(k,(c[0],c[1]), fontsize = fontSize) # make branches if (k == (len(circles)-1)/n): k = 0 k += 1 return numList def addLinesToPlot(n, circles): lineList = Graphics() for x in range(0, len(circles) - 1): lineList += line([(circles[x][0],circles[x][1]),(circles[x+1][0],circles[x+1][1])]) return lineList 
       
%time plots = Graphics() colors = ['0066cc', 'cc0000', 'ffcc66'] # need to be in order of: First circle, second circle, third circle, in terms of the starting 3 circles and a top down reading of the matrix. p = Profiler() p("create circles") createCircles(8, 6, 6, True, colors) # n, maxDepth, maxCDepth, withC, color list p() print p 
       
from PIL import Image, ImageDraw import csv size = 10800 scaleFactor = size/3.6 def makeCircle(c, im, i): draw = ImageDraw.Draw(im) x = int(round(size/2 + sage_eval(c[0])*scaleFactor)) y = int(round(size/2 - sage_eval(c[1])*scaleFactor)) r = int(round(1/sage_eval(c[2])*scaleFactor)) draw.ellipse((x-r, y-r, x+r, y+r), fill='#'+c[3]) del draw if (i % 100000 == 0): print "hi" if (i % 1000000 == 0): im.save(DATA + 'test.png', "PNG") print "saved" img = Image.new('RGBA',(size, size)) img.save(DATA + 'test.png', 'PNG') im = Image.open(DATA + "test.png") with open(DATA +'test.csv', 'rb') as csvfile: print "here!" reader = csv.reader(csvfile, delimiter=',') i = 0 for c in reader: makeCircle(c, im, i) i += 1 im.save(DATA + 'test.png', "PNG") 
       
import csv fits = [] for n in range (4, 8): q = 0 w = 0 e = 0 with open(DATA +'test.csv', 'rb') as csvfile: reader = csv.reader(csvfile, delimiter=',') for c in reader: if (float(c[2]) <= 100): q += 1 if (float(c[2]) <= 1000): w += 1 if (float(c[2]) <= 10000): e += 1 points = [] points.append([N(ln(100)), N(ln(q))]) points.append([N(ln(1000)), N(ln(w))]) points.append([N(ln(10000)), N(ln(e))]) var('a,b') model(x) = a*x+b fits += find_fit(points,model) print find_fit(points,model) point(points)+plot(model(a=find_fit(points,model)[0].rhs(),b=find_fit(points,model)[1].rhs()),(x,0,10),color='red') 
       
def createCirclesWithoutColors(n, maxDepth, maxCDepth, withC): class CircleInfo: def __init__(self, S, depth, depthBeforeC, lastOne, initialC, isC, isFirstC): self.S = S self.lastOne = lastOne self.initialC = initialC self.depth = depth self.depthBeforeC = depthBeforeC self.isC = isC self.isFirstC = isFirstC # precompute powers of A and B to reduce amount of matrix multiplication - cut time in half A = [] for x in range(0,n): A.append(N(createCirclesAround(n))^x) B = [] for x in range(0,3): B.append(N(changeHub(n))^x) C = N(changePerspective(n)) AB = A[1]*B[1] #A*B BC = B[1]*C #B*C BBC = B[2]*C #B^2*C startVals = N(startingValues(n)) stack = [] f = file(DATA + 'test.csv', 'w') curvature = (startVals)[0][2] xCoord = (startVals)[0][0]/curvature yCoord = (startVals)[0][1]/curvature circle = '%.30f' % xCoord + ',' + '%.30f' % yCoord + ',' + '%.30f' % curvature + '\r\n' f.write(circle) stack.append(CircleInfo(startVals, 0, 0, False, True, False, True)) while (stack != []): pop = stack.pop() depth = pop.depth depthBeforeC = pop.depthBeforeC initialC = pop.initialC isC = pop.isC isFirstC = pop.isFirstC lastOne = pop.lastOne S = pop.S if (isC and isFirstC and depth > 0): depthBeforeC = depth depth = 1 isFirstC = False if (not isC and depth >= maxDepth): continue elif (isC and depth >= maxCDepth - depthBeforeC + 2): continue elif (isC and depth >= 4): continue if (depth == 0): lower = 0 upper = n elif (initialC): lower = 2 upper = n - 1 initialC = False elif (depth > 1 and lastOne): lower = 2 upper = n - 3 lastOne = False if (withC): Z = AB*S stack.append(CircleInfo(C*Z, depth, depthBeforeC, False, True, True, isFirstC)) stack.append(CircleInfo(BC*Z, depth, depthBeforeC, False, True, True, isFirstC)) stack.append(CircleInfo(BBC*Z, depth, depthBeforeC, False, True, True, isFirstC)) else: lower = 2 upper = n - 2 for x in range(lower, upper): Z = A[x]*S curvature = (Z)[2][2] xCoord = (Z)[2][0]/curvature yCoord = (Z)[2][1]/curvature circle = '%.30f' % xCoord + ',' + '%.30f' % yCoord + ',' + '%.30f' % curvature + '\r\n' f.write(circle) if (withC): stack.append(CircleInfo(C*Z, depth+1, depthBeforeC, False, True, True, isFirstC)) stack.append(CircleInfo(BC*Z, depth+1, depthBeforeC, False, True, True, isFirstC)) stack.append(CircleInfo(BBC*Z, depth+1, depthBeforeC, False, True, True, isFirstC)) stack.append(CircleInfo(B[2]*Z, depth+1, depthBeforeC, x == upper - 1, False, isC, isFirstC)) if (withC and depth == maxDepth - 1): Z = A[upper]*S stack.append(CircleInfo(C*Z, depth+1, depthBeforeC, False, True, True, isFirstC)) stack.append(CircleInfo(BC*Z, depth+1, depthBeforeC, False, True, True, isFirstC)) stack.append(CircleInfo(BBC*Z, depth+1, depthBeforeC, False, True, True, isFirstC))