def param(xlist, ylist, vw=ViewWindow(), colorlist=None, auto=False, gif=False, add=False, avg=False,
filename="param" + str(int(time())), save=True):
if callable(xlist):
xlist = [xlist]
if callable(ylist):
ylist = [ylist]
if auto:
vw.autoparam(xlist, ylist)
data = PlotData(vw)
images = []
color = 0
if colorlist is None:
colorlist = Color.colors(len(xlist))
for i in range(len(xlist)):
x = xlist[i]
y = ylist[i]
t = vw.tmin
if colorlist != 'rainbow':
color = colorlist[i]
while t <= vw.tmax:
if colorlist == 'rainbow':
color = Color.rbow(vw.tmax - t, 2)
u = t + vw.tstep
data.line0((x(t), y(t)), (x(u), y(u)), color, add, avg)
t = u
if gif:
images.append(data.save("", False))
if gif:
writegif(filename, images, 0.01)
return data.save(filename, save)
def gridspanningtree(length, height, d=2, r=0, color=Color(255, 0, 0), g="grid", filename=None, treefunc="dfs", gif=False,
save=True):
images = []
if not isinstance(g, Graph):
(x, y) = (randint(0, length - 1), randint(0, height - 1))
g = getattr(Graph, g)(length, height).treefunc(treefunc, (x, y))
else:
(x, y) = list(g.dict.keys)[0]
vw = ViewWindow(dimx=d * length + d - 1, dimy=d * height + d - 1)
data = PlotData(vw)
color2 = 0.8 * color
for v1 in g.dict:
for i in range(-r, r + 1):
for j in range(-r, r + 1):
data.putpixel((d * (v1[0] + 1) - 1 + i, d * (v1[1] + 1) - 1 + j), color)
s = {(x, y)}
q = [(x, y)]
while q:
v1 = q.pop(0)
for v2 in g.dict[v1]:
if v2 not in s:
for i in range(1 + r, d - r):
data.putpixel(
(d * (v1[0] + 1) - 1 + (v2[0] - v1[0]) * i, d * (v1[1] + 1) - 1 + (v2[1] - v1[1]) * i), color2)
q.append(v2)
s.add(v2)
if gif:
images.append(data.save("", False))
if filename is None:
filename = "gst " + str((length, height)) + " " + str(int(time()))
ret = data.save(filename, save)
if gif:
writegif(filename, images, 0.01)
return ret
def gridspanningtree2(length, height, d=2, r=0, g="grid", color=Color(255, 0, 0), filename=None, treefunc=None, func="dfs",
gif=False,
save=True):
images = []
if not isinstance(g, Graph):
g = getattr(Graph, g)(length, height)
if treefunc is not None:
(x, y) = (randint(0, length - 1), randint(0, height - 1))
g = g.treefunc(treefunc, (x, y))
(x, y) = (randint(0, length - 1), randint(0, height - 1))
g = g.func(func, (x, y))
vw = ViewWindow(dimx=d * length + d - 1, dimy=d * height + d - 1)
data = PlotData(vw)
color2 = 0.8 * color
for p in g:
try:
for i in range(-r, r + 1):
for j in range(-r, r + 1):
data.putpixel((d * (p[0] + 1) - 1 + i, d * (p[1] + 1) - 1 + j), color)
except TypeError:
for i in range(-r, r + 1):
for j in range(-r, r + 1):
data.putpixel((d * (p[1][0] + 1) - 1 + i, d * (p[1][1] + 1) - 1 + j), color)
for i in range(1 + r, d - r):
data.putpixel(
(d * (p[0][0] + 1) - 1 + (p[1][0] - p[0][0]) * i, d * (p[0][1] + 1) - 1 + (p[1][1] - p[0][1]) * i),
color2)
if gif:
images.append(data.save("", False))
if filename is None:
filename = "gst2 " + str((length, height)) + " " + str(time())
ret = data.save(filename, save)
if gif:
writegif(filename, images, 0.01)
return ret
def funcgraph(funclist, vw=ViewWindow(), colorlist=None, auto=False, filename="plot" + str(int(time())), gif=False,
add=False, avg=False, save=True):
images = []
if auto:
vw.autograph(funclist)
if callable(funclist):
funclist = [funclist]
data = PlotData(vw)
if colorlist is None:
colorlist = Color.colors(len(funclist))
for j in range(len(funclist)):
f = funclist[j]
it = vw.xiterator()
x0 = it.next()
for x1 in it:
if colorlist == "rainbow":
color = Color.rbow(x1, 2)
else:
color = colorlist[j]
data.line((x0, f(x0)), (x1, f(x1)), color, add, avg)
x0 = x1
if gif:
images.append(data.save("", False))
if gif:
writegif(filename, images, 0.01)
return data.save(filename, save)
def zrotate(xlist, ylist, vw=ViewWindow(), segs=4, colorlist=None, auto=False, filename=None, gif=False, add=True,
avg=False, save=True):
if auto:
vw.autoparam(xlist, ylist)
if filename is None:
filename = "zrotate" + str(int(time()))
if callable(xlist):
xlist = [xlist]
if callable(ylist):
ylist = [ylist]
data = PlotData(vw, "rainbow" if colorlist == "rainbow" else Color(0, 0, 0))
images = []
if colorlist is None:
colorlist = Color.colors(len(xlist))
tlist = [vw.tmin + (vw.tmax - vw.tmin) * j / segs for j in range(segs + 1)]
while tlist[0] < vw.tmax:
for (x, y, color) in zip(xlist, ylist, colorlist):
if colorlist == 'rainbow':
color = Color.rbow(tlist[0], segs)
for j in range(len(tlist) - 1):
data.line0((x(tlist[j]), y(tlist[j])), (x(tlist[j + 1]), y(tlist[j + 1])), color, add, avg)
if gif:
images.append(data.save("", False))
tlist = [t + vw.tstep for t in tlist]
if gif:
writegif(filename, images, 0.01)
return data.save(filename, save)
def funcgraph(funclist,
vw=ViewWindow(),
colorlist=None,
auto=False,
filename="plot" + str(int(time())),
gif=False,
add=False,
avg=False,
save=True):
images = []
if auto:
vw.autograph(funclist)
if callable(funclist):
funclist = [funclist]
data = PlotData(vw)
if colorlist is None:
colorlist = Color.colors(len(funclist))
for j in range(len(funclist)):
f = funclist[j]
it = vw.xiterator()
x0 = it.next()
for x1 in it:
if colorlist == "rainbow":
color = Color.rbow(x1, 2)
else:
color = colorlist[j]
data.line((x0, f(x0)), (x1, f(x1)), color, add, avg)
x0 = x1
if gif:
images.append(data.save("", False))
if gif:
writegif(filename, images, 0.01)
return data.save(filename, save)
def juliazoom(f, vw, z0=0, factor=1.5, frames=20, n=50, duration=0.5, zmax=2, color=Color(255, 0, 0), filename=None):
images = []
for i in range(frames):
vw = ViewWindow(z0.real - factor ** -i, z0.real + factor ** -i, z0.imag - factor ** -i, z0.imag + factor ** -i,
dimx=vw.dimx, dimy=vw.dimy)
images.append(julia(f, vw, n, zmax, color, filename, False))
if filename is None:
filename = "julia " + str(n) + " " + str(zmax) + " " + str(int(time()))
writegif(filename, images, duration)
def gridspanningtree2(length,
height,
d=2,
r=0,
g="grid",
color=Color(255, 0, 0),
filename=None,
treefunc=None,
func="dfs",
gif=False,
save=True):
images = []
if not isinstance(g, Graph):
g = getattr(Graph, g)(length, height)
if treefunc is not None:
(x, y) = (randint(0, length - 1), randint(0, height - 1))
g = g.treefunc(treefunc, (x, y))
(x, y) = (randint(0, length - 1), randint(0, height - 1))
g = g.func(func, (x, y))
vw = ViewWindow(dimx=d * length + d - 1, dimy=d * height + d - 1)
data = PlotData(vw)
color2 = 0.8 * color
for p in g:
try:
for i in range(-r, r + 1):
for j in range(-r, r + 1):
data.putpixel(
(d * (p[0] + 1) - 1 + i, d * (p[1] + 1) - 1 + j),
color)
except TypeError:
for i in range(-r, r + 1):
for j in range(-r, r + 1):
data.putpixel(
(d * (p[1][0] + 1) - 1 + i, d * (p[1][1] + 1) - 1 + j),
color)
for i in range(1 + r, d - r):
data.putpixel(
(d * (p[0][0] + 1) - 1 + (p[1][0] - p[0][0]) * i, d *
(p[0][1] + 1) - 1 + (p[1][1] - p[0][1]) * i), color2)
if gif:
images.append(data.save("", False))
if filename is None:
filename = "gst2 " + str((length, height)) + " " + str(time())
ret = data.save(filename, save)
if gif:
writegif(filename, images, 0.01)
return ret
def graphpict(length, height, graphtype="grid", treefunc="dfs", func="bfs", colorfunc="hilbert", gif=False, gifres=None, v0=None, v1=None,
rand=True, save=True, scales=None):
images = []
clist = []
if isinstance(graphtype, Graph):
area = len(graphtype.dict)
else:
area = length * height
if not colorfunc.startswith("rbow"):
clist = colorcube(colorfunc)
if func == "hilbert":
l = hilbert(int(ceil(log(max(length, height), 2))))
gstr = "None"
else:
if not isinstance(graphtype, Graph):
gstr = graphtype
graphtype = getattr(Graph, graphtype)(length, height)
else:
gstr = "Graph"
if v0 is None:
v0 = choice(graphtype.dict.keys())
if treefunc is not None:
if v1 is None:
v1 = choice(graphtype.dict.keys())
graphtype = graphtype.treefunc(treefunc, v1, rand)
print "Computed spanning tree"
l = graphtype.func(func, v0, rand)
if gif and gifres is None:
gifres = ceil(area / 150.0)
vw = ViewWindow(dimx=length, dimy=height)
data = PlotData(vw, scales=scales)
i = 0
for p in l:
if colorfunc.startswith("rbow"):
data.putpixel(p, getattr(Color, colorfunc)(2 * pi * i / area, 1))
else:
data.putpixel(p, Color(*[c * 4 for c in clist[min(64 ** 3 * i / area, 64 ** 3 - 1)]]))
if gif and (i + 1) % gifres == 0:
images.append(data.save("", False))
i += 1
filename = str((length, height)) + " " + gstr + " spanningtree" + str(treefunc) + " " + func + " " + colorfunc + " " + str(
rand) + " " + str((v0, v1)) + " " + str(int(time()))
ret = data.save(filename, save)
if gif:
writegif(filename, images, 0.001)
return ret
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 gridspanningtree(length,
height,
d=2,
r=0,
color=Color(255, 0, 0),
g="grid",
filename=None,
treefunc="dfs",
gif=False,
save=True):
images = []
if not isinstance(g, Graph):
(x, y) = (randint(0, length - 1), randint(0, height - 1))
g = getattr(Graph, g)(length, height).treefunc(treefunc, (x, y))
else:
(x, y) = list(g.dict.keys)[0]
vw = ViewWindow(dimx=d * length + d - 1, dimy=d * height + d - 1)
data = PlotData(vw)
color2 = 0.8 * color
for v1 in g.dict:
for i in range(-r, r + 1):
for j in range(-r, r + 1):
data.putpixel(
(d * (v1[0] + 1) - 1 + i, d * (v1[1] + 1) - 1 + j), color)
s = {(x, y)}
q = [(x, y)]
while q:
v1 = q.pop(0)
for v2 in g.dict[v1]:
if v2 not in s:
for i in range(1 + r, d - r):
data.putpixel(
(d * (v1[0] + 1) - 1 + (v2[0] - v1[0]) * i, d *
(v1[1] + 1) - 1 + (v2[1] - v1[1]) * i), color2)
q.append(v2)
s.add(v2)
if gif:
images.append(data.save("", False))
if filename is None:
filename = "gst " + str((length, height)) + " " + str(int(time()))
ret = data.save(filename, save)
if gif:
writegif(filename, images, 0.01)
return ret
def juliazoom(f,
vw,
z0=0,
factor=1.5,
frames=20,
n=50,
duration=0.5,
zmax=2,
color=Color(255, 0, 0),
filename=None):
images = []
for i in range(frames):
vw = ViewWindow(z0.real - factor**-i,
z0.real + factor**-i,
z0.imag - factor**-i,
z0.imag + factor**-i,
dimx=vw.dimx,
dimy=vw.dimy)
images.append(julia(f, vw, n, zmax, color, filename, False))
if filename is None:
filename = "julia " + str(n) + " " + str(zmax) + " " + str(int(time()))
writegif(filename, images, duration)
def param(xlist,
ylist,
vw=ViewWindow(),
colorlist=None,
auto=False,
gif=False,
add=False,
avg=False,
filename="param" + str(int(time())),
save=True):
if callable(xlist):
xlist = [xlist]
if callable(ylist):
ylist = [ylist]
if auto:
vw.autoparam(xlist, ylist)
data = PlotData(vw)
images = []
color = 0
if colorlist is None:
colorlist = Color.colors(len(xlist))
for i in range(len(xlist)):
x = xlist[i]
y = ylist[i]
t = vw.tmin
if colorlist != 'rainbow':
color = colorlist[i]
while t <= vw.tmax:
if colorlist == 'rainbow':
color = Color.rbow(vw.tmax - t, 2)
u = t + vw.tstep
data.line0((x(t), y(t)), (x(u), y(u)), color, add, avg)
t = u
if gif:
images.append(data.save("", False))
if gif:
writegif(filename, images, 0.01)
return data.save(filename, save)
def zrotate(xlist,
ylist,
vw=ViewWindow(),
segs=4,
colorlist=None,
auto=False,
filename=None,
gif=False,
add=True,
avg=False,
save=True):
if auto:
vw.autoparam(xlist, ylist)
if filename is None:
filename = "zrotate" + str(int(time()))
if callable(xlist):
xlist = [xlist]
if callable(ylist):
ylist = [ylist]
data = PlotData(vw,
"rainbow" if colorlist == "rainbow" else Color(0, 0, 0))
images = []
if colorlist is None:
colorlist = Color.colors(len(xlist))
tlist = [vw.tmin + (vw.tmax - vw.tmin) * j / segs for j in range(segs + 1)]
while tlist[0] < vw.tmax:
for (x, y, color) in zip(xlist, ylist, colorlist):
if colorlist == 'rainbow':
color = Color.rbow(tlist[0], segs)
for j in range(len(tlist) - 1):
data.line0((x(tlist[j]), y(tlist[j])),
(x(tlist[j + 1]), y(tlist[j + 1])), color, add, avg)
if gif:
images.append(data.save("", False))
tlist = [t + vw.tstep for t in tlist]
if gif:
writegif(filename, images, 0.01)
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 graphpict(length,
height,
graphtype="grid",
treefunc="dfs",
func="bfs",
colorfunc="hilbert",
gif=False,
gifres=None,
v0=None,
v1=None,
rand=True,
save=True,
scales=None):
images = []
clist = []
if isinstance(graphtype, Graph):
area = len(graphtype.dict)
else:
area = length * height
if not colorfunc.startswith("rbow"):
clist = colorcube(colorfunc)
if func == "hilbert":
l = hilbert(int(ceil(log(max(length, height), 2))))
gstr = "None"
else:
if not isinstance(graphtype, Graph):
gstr = graphtype
graphtype = getattr(Graph, graphtype)(length, height)
else:
gstr = "Graph"
if v0 is None:
v0 = choice(graphtype.dict.keys())
if treefunc is not None:
if v1 is None:
v1 = choice(graphtype.dict.keys())
graphtype = graphtype.treefunc(treefunc, v1, rand)
print "Computed spanning tree"
l = graphtype.func(func, v0, rand)
if gif and gifres is None:
gifres = ceil(area / 150.0)
vw = ViewWindow(dimx=length, dimy=height)
data = PlotData(vw, scales=scales)
i = 0
for p in l:
if colorfunc.startswith("rbow"):
data.putpixel(p, getattr(Color, colorfunc)(2 * pi * i / area, 1))
else:
data.putpixel(
p,
Color(
*[c * 4 for c in clist[min(64**3 * i / area, 64**3 - 1)]]))
if gif and (i + 1) % gifres == 0:
images.append(data.save("", False))
i += 1
filename = str((length, height)) + " " + gstr + " spanningtree" + str(
treefunc) + " " + func + " " + colorfunc + " " + str(rand) + " " + str(
(v0, v1)) + " " + str(int(time()))
ret = data.save(filename, save)
if gif:
writegif(filename, images, 0.001)
return ret