def critK(d, farey, wantPlot=False):
kGuess = -math.log(1 / (2 * d) - 1) / math.log(2) # if 0, 1/2 overlap
step = 1.0
while True:
if max(getP(d, kGuess, farey)[1]) == 0:
kGuess = kGuess + step
else:
if step < 1e-5:
break
else:
kGuess = kGuess - step
step = step / 10.0
if wantPlot:
xK, pK, gradpK = getP(d, kGuess + step, farey)
plot(xK, gradpK, label="A little pressure", linewidth=2)
xM, pM, gradpM = getP(d, kGuess - step, farey)
plot(xM, gradpM, "r", label="No Pressure")
ylim((-0.1, 1.1))
legend()
show()
x, p, gradp = getP(d, kGuess + step, farey)
return kGuess, (x[3] + x[2]) / 2 # last irrational < 0.5
from pylab import *
import numpy as np
from fractal import getP #(d, k, nmax), returns x, p, gradp
from scipy.interpolate import interp1d
x, p, gradp = getP(0.1, 2, 200)
def getLength(x,p,r):
newX = np.arange(0,1,0.0001)
newP = interp1d(x,p)
xs, ys = [x[0]], [p[0]]
theta = np.arange(0,np.pi/2.,0.001)
length = 0
while xs[-1] + r < 1:
xNow = xs[-1] + r*np.cos(theta)
yNow = ys[-1] + r*np.sin(theta)
pNow = newP(xNow)
match = np.argwhere(np.isclose(yNow,pNow, atol=0.0005))
match = round(np.mean(match))
xs.append(xNow[match])
ys.append(yNow[match])
length += r
remaining = sqrt((xs[-1]-1)**2+(ys[-1]-p[-1])**2)
length += remaining
return length
lengths = []
rs = [1,.1, .01, .001, .0001, 1e-5]
for r in rs:
from pylab import *
import numpy as np
from fractal import getP
nmax = 100
drange = np.arange(0,.51,0.005)
krange = np.arange(1, 4.02,0.01)
lenD, lenK = len(drange), len(krange)
storeP = np.zeros((lenD,lenK,nmax))
clf()
cmap = get_cmap('RdBu')
cmap.set_under('black')
cmap.set_over('green')
for n in range(1,nmax):
for d in range(lenD):
for k in range(lenK):
storeP[d,k,n-1] = max(getP(drange[d],krange[k],n)[1])
pcolor(krange,drange,storeP[:,:,n-1],cmap=cmap,vmin=0.001,vmax=.999)
title('Max pressure at Farey level '+str(n))
colorbar(extend='both')
ylim(0,.5)
xlim(1,4)
savefig('C:/Users/bkraus/Dropbox/Hudson/Images_dkMaps_020516/dk'+str(n)+'.jpg')
clf()