def basin3(f,
rootlist,
colorlist=None,
vw=ViewWindow(),
df=None,
n=10,
dots=True,
filename="basin" + str(int(time())),
save=True):
if df is None:
df = diffquo(f, .0001)
if colorlist is None:
colorlist = Color.colors(len(rootlist))
data = PlotData(vw)
for i in range(vw.dimx):
for j in range(vw.dimy):
z = vw.xpxcart(i) + vw.ypxcart(j) * 1j
for k in range(n + 1):
data.putpixel((i, j),
colorlist[closest(rootlist, z)],
add=True,
avg=True)
if k != n:
z = newton(f, z, df, 1)
if dots:
for r in rootlist:
data.putpoint((r.real, r.imag), 0)
return data.save(filename, save)
def basin2(f,
rootlist,
colorlist=None,
vw=ViewWindow(),
df=None,
n=10,
dots=True,
filename="basin2" + str(int(time())),
dist=0.3,
save=True):
if df is None:
df = diffquo(f, .0001)
if colorlist is None:
colorlist = Color.colors(len(rootlist))
data = PlotData(vw)
for i in range(vw.dimx):
for j in range(vw.dimy):
z = vw.xpxcart(i) + vw.ypxcart(j) * 1j
for k in range(n):
z = newton(f, z, df, 1)
index = closest(rootlist, z)
d = abs(z - rootlist[index])
if d < dist or k == n - 1:
data.putpixel((i, j),
max(.2, 1 - float(k) / n) * colorlist[index])
break
if dots:
for r in rootlist:
data.putpoint((r.real, r.imag), 0)
return data.save(filename, save)
def complexroots(deg, vw, color=Color(5, 0, 0), coeffs=(-1, 1), filename=None, save=True):
if np is None:
raise Exception()
data = PlotData(vw)
for i, l in enumerate(product(coeffs, repeat=deg + 1)):
if i % len(coeffs) ** (deg - 4) == 0:
print float(i) / 2 ** (deg + 1)
for root in np.roots(l):
data.putpoint((root.real, root.imag), color, True)
if filename is None:
filename = "complexroots " + str(deg) + " " + str(int(time()))
return data.save(filename, save)
def voronoi(rootlist, colorlist=None, vw=ViewWindow(), dots=True, metric=lp(2), select=1,
filename="voronoi" + str(int(time())), save=True):
if colorlist is None:
colorlist = Color.colors(len(rootlist))
data = PlotData(vw)
for i in range(vw.dimx):
for j in range(vw.dimy):
data.putpixel((i, j), colorlist[closest(rootlist, vw.xpxcart(i) + vw.ypxcart(j) * 1j, metric, select)])
if dots:
for r in rootlist:
data.putpoint((r.real, r.imag), 0)
return data.save(filename, save)
def basin(f, rootlist, colorlist=None, vw=ViewWindow(), df=None, n=10, dots=True,
filename="basin" + str(int(time())), save=True):
if df is None:
df = diffquo(f, .0001)
if colorlist is None:
colorlist = Color.colors(len(rootlist))
data = PlotData(vw)
for i in range(vw.dimx):
for j in range(vw.dimy):
data.putpixel((i, j), colorlist[closest(rootlist, newton(f, vw.xpxcart(i) + vw.ypxcart(j) * 1j, df, n))])
if dots:
for r in rootlist:
data.putpoint((r.real, r.imag), 0)
return data.save(filename, save)
def complexroots(deg,
vw,
color=Color(5, 0, 0),
coeffs=(-1, 1),
filename=None,
save=True):
if np is None:
raise Exception()
data = PlotData(vw)
for i, l in enumerate(product(coeffs, repeat=deg + 1)):
if i % len(coeffs)**(deg - 4) == 0:
print float(i) / 2**(deg + 1)
for root in np.roots(l):
data.putpoint((root.real, root.imag), color, True)
if filename is None:
filename = "complexroots " + str(deg) + " " + str(int(time()))
return data.save(filename, save)
def newtondist(f, vw=ViewWindow(), df=None, n=1, pxdist=1, filename="newtondist" + str(int(time()))):
images = []
if df is None:
df = diffquo(f, .0001)
col = Color.colors(vw.dimx * vw.dimy)
for k in range(6):
data = PlotData(vw)
for i in range(vw.dimx):
for j in range(vw.dimy):
if i % pxdist == 0 and j % pxdist == 0:
z0 = vw.xpxcart(i) + 1j * vw.ypxcart(j)
z = newton(f, z0, df, n, 1e-1)
z0 = newton(f, z0, df, n - 1, 1e-1)
data.putpoint(((k * z.real + (5 - k) * z0.real) / 5, (k * z.imag + (5 - k) * z0.imag) / 5),
col[i + j * vw.dimx])
images.append(data.save("", False))
writegif(filename, images, 1)
return images[-1]
def basin2(f, rootlist, colorlist=None, vw=ViewWindow(), df=None, n=10, dots=True,
filename="basin2" + str(int(time())), dist=0.3, save=True):
if df is None:
df = diffquo(f, .0001)
if colorlist is None:
colorlist = Color.colors(len(rootlist))
data = PlotData(vw)
for i in range(vw.dimx):
for j in range(vw.dimy):
z = vw.xpxcart(i) + vw.ypxcart(j) * 1j
for k in range(n):
z = newton(f, z, df, 1)
index = closest(rootlist, z)
d = abs(z - rootlist[index])
if d < dist or k == n - 1:
data.putpixel((i, j), max(.2, 1 - float(k) / n) * colorlist[index])
break
if dots:
for r in rootlist:
data.putpoint((r.real, r.imag), 0)
return data.save(filename, save)
def voronoi(rootlist,
colorlist=None,
vw=ViewWindow(),
dots=True,
metric=lp(2),
select=1,
filename="voronoi" + str(int(time())),
save=True):
if colorlist is None:
colorlist = Color.colors(len(rootlist))
data = PlotData(vw)
for i in range(vw.dimx):
for j in range(vw.dimy):
data.putpixel((i, j),
colorlist[closest(rootlist,
vw.xpxcart(i) + vw.ypxcart(j) * 1j,
metric, select)])
if dots:
for r in rootlist:
data.putpoint((r.real, r.imag), 0)
return data.save(filename, save)
def newtondist(f,
vw=ViewWindow(),
df=None,
n=1,
pxdist=1,
filename="newtondist" + str(int(time()))):
images = []
if df is None:
df = diffquo(f, .0001)
col = Color.colors(vw.dimx * vw.dimy)
for k in range(6):
data = PlotData(vw)
for i in range(vw.dimx):
for j in range(vw.dimy):
if i % pxdist == 0 and j % pxdist == 0:
z0 = vw.xpxcart(i) + 1j * vw.ypxcart(j)
z = newton(f, z0, df, n, 1e-1)
z0 = newton(f, z0, df, n - 1, 1e-1)
data.putpoint(((k * z.real + (5 - k) * z0.real) / 5,
(k * z.imag + (5 - k) * z0.imag) / 5),
col[i + j * vw.dimx])
images.append(data.save("", False))
writegif(filename, images, 1)
return images[-1]