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 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 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 polarshade(r1,
r2,
vw=ViewWindow(),
color=None,
auto=False,
filename="polarshade" + str(int(time())),
save=True):
if auto:
vw.autoparam(
[lambda t0: r1(t0) * cos(t0), lambda t0: r2(t0) * cos(t0)],
[lambda t0: r1(t0) * sin(t0), lambda t0: r2(t0) * sin(t0)])
data = PlotData(vw)
th = vw.thick * (vw.xmax - vw.xmin) / vw.dimx
if color is None:
c = Color(255, 0, 0)
else:
c = color
for i in range(vw.dimx):
x = vw.xpxcart(i)
for j in range(vw.dimy):
y = vw.ypxcart(j)
t = atan2(y, x)
r = sqrt(x**2 + y**2)
if color == 'rainbow':
c = Color.rbow(t)
if r1(t) - th <= r <= r2(t) + th or r2(t) - th <= r <= r1(t) + th:
data.putpixel((i, j), c)
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 color3d(f, vw=ViewWindow(), base=1.0, pos=Color(255, 0, 0), neg=Color(0, 0, 255),
filename="color3d" + str(int(time())), save=True):
data = PlotData(vw)
for i in range(vw.dimx):
for j in range(vw.dimy):
(x, y) = vw.px2cart((i, j))
color = Color()
val = f((x, y))
if val > 0:
color = abs(val / base) * pos
if val < 0:
color = abs(val / base) * neg
data.putpixel((i, j), color)
return data.save(filename, save)
def mandelbrot(vw=ViewWindow(xmin=-2.3, xmax=0.7, ymin=-1.5, ymax=1.5, dimx=700, dimy=701), n=50, reflect=True,
color=Color(255, 0, 0), filename=None, save=True):
data = PlotData(vw)
color0 = color
if callable(color):
colorfunc = color
else:
colorfunc = lambda t: t * color0
for p in vw.pxiterator():
c = vw.xpxcart(p[0]) + vw.ypxcart(p[1]) * 1j
if c.imag > -0.1 or not reflect:
i, z0 = 0, 0
q = (c.real - 0.25) ** 2 + c.imag ** 2
if q * (q + (c.real - 0.25)) < c.imag ** 2 / 4 or 16 * ((c.real + 1) ** 2 + c.imag ** 2) < 1:
data.putpixel(p, colorfunc(1.0), flip=False)
if reflect:
data.putpixel((p[0], vw.ycartpx(-c.imag)), colorfunc(1.0), flip=False)
else:
while abs(z0) < 2 and i < n:
z0 = z0 * z0 + c
i += 1
data.putpixel(p, colorfunc(float(i) / n), flip=False)
if reflect:
data.putpixel((p[0], vw.ycartpx(-c.imag)), colorfunc(float(i) / n), flip=False)
else:
break
if PYGAME_PIXEL and p[0] == 0:
pygame.display.flip()
if filename is None:
filename = "mandelbrot " + str(n) + " " + str(int(time()))
return data.save(filename, save)
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 newtondiff(f, vw=ViewWindow(), df=None, n=1, pxdist=1, filename="newtondiff" + str(int(time())), save=True):
if df is None:
df = diffquo(f, .0001)
data = PlotData(vw)
color1 = Color(0, 255, 0)
color2 = Color(255, 0, 0)
for i in range(vw.dimx):
for j in range(vw.dimy):
if i % pxdist == 0 and j % pxdist == 0:
z0 = vw.xpxcart(i) + vw.ypxcart(j) * 1j
z = newton(f, z0, df, n, 1e-1)
if abs(z) < abs(z0):
color = color1
else:
color = color2
data.putpixel((i, j), color)
return data.save(filename, save)
def implicit(flist, vw=ViewWindow(), decay=100, colorlist=None, filename="implicit" + str(int(time())), save=True):
data = PlotData(vw)
color = 0
if colorlist is None:
colorlist = Color.colors(len(flist))
for k in range(len(flist)):
f = flist[k]
if colorlist != "rainbow":
color = colorlist[k]
for i in range(vw.dimx):
for j in range(vw.dimy):
if colorlist == "rainbow":
color = Color.rbow(vw.xpxcart(i) + vw.ypxcart(j), 2)
color0 = e ** (-decay * abs(f(*vw.px2cart((i, j))))) * color
color0 += data[(i, j)]
data.putpixel((i, j), color0)
return data.save(filename, save)
def julia(f, vw, n=50, zmax=2, color=Color(255, 0, 0), filename=None, save=True):
data = PlotData(vw)
if callable(color):
colorfunc = color
else:
colorfunc = lambda t: t * color
for p in vw.pxiterator():
z = vw.xpxcart(p[0]) + vw.ypxcart(p[1]) * 1j
i = 0
while abs(z) < zmax and i < n:
z = f(z)
i += 1
data.putpixel(p, colorfunc(float(i) / n), flip=False)
if PYGAME_PIXEL and p[0] == 0:
pygame.display.flip()
if filename is None:
filename = "julia " + str(n) + " " + str(zmax) + " " + str(int(time()))
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 color3d(f,
vw=ViewWindow(),
base=1.0,
pos=Color(255, 0, 0),
neg=Color(0, 0, 255),
filename="color3d" + str(int(time())),
save=True):
data = PlotData(vw)
for i in range(vw.dimx):
for j in range(vw.dimy):
(x, y) = vw.px2cart((i, j))
color = Color()
val = f((x, y))
if val > 0:
color = abs(val / base) * pos
if val < 0:
color = abs(val / base) * neg
data.putpixel((i, j), color)
return data.save(filename, save)
def polarshade(r1, r2, vw=ViewWindow(), color=None, auto=False, filename="polarshade" + str(int(time())), save=True):
if auto:
vw.autoparam([lambda t0: r1(t0) * cos(t0), lambda t0: r2(t0) * cos(t0)],
[lambda t0: r1(t0) * sin(t0), lambda t0: r2(t0) * sin(t0)])
data = PlotData(vw)
th = vw.thick * (vw.xmax - vw.xmin) / vw.dimx
if color is None:
c = Color(255, 0, 0)
else:
c = color
for i in range(vw.dimx):
x = vw.xpxcart(i)
for j in range(vw.dimy):
y = vw.ypxcart(j)
t = atan2(y, x)
r = sqrt(x ** 2 + y ** 2)
if color == 'rainbow':
c = Color.rbow(t)
if r1(t) - th <= r <= r2(t) + th or r2(t) - th <= r <= r1(t) + th:
data.putpixel((i, j), c)
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 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 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 implicit(flist,
vw=ViewWindow(),
decay=100,
colorlist=None,
filename="implicit" + str(int(time())),
save=True):
data = PlotData(vw)
color = 0
if colorlist is None:
colorlist = Color.colors(len(flist))
for k in range(len(flist)):
f = flist[k]
if colorlist != "rainbow":
color = colorlist[k]
for i in range(vw.dimx):
for j in range(vw.dimy):
if colorlist == "rainbow":
color = Color.rbow(vw.xpxcart(i) + vw.ypxcart(j), 2)
color0 = e**(-decay * abs(f(*vw.px2cart((i, j))))) * color
color0 += data[(i, j)]
data.putpixel((i, j), color0)
return data.save(filename, save)
def newtondiff(f,
vw=ViewWindow(),
df=None,
n=1,
pxdist=1,
filename="newtondiff" + str(int(time())),
save=True):
if df is None:
df = diffquo(f, .0001)
data = PlotData(vw)
color1 = Color(0, 255, 0)
color2 = Color(255, 0, 0)
for i in range(vw.dimx):
for j in range(vw.dimy):
if i % pxdist == 0 and j % pxdist == 0:
z0 = vw.xpxcart(i) + vw.ypxcart(j) * 1j
z = newton(f, z0, df, n, 1e-1)
if abs(z) < abs(z0):
color = color1
else:
color = color2
data.putpixel((i, j), color)
return data.save(filename, save)
def julia(f,
vw,
n=50,
zmax=2,
color=Color(255, 0, 0),
filename=None,
save=True):
data = PlotData(vw)
if callable(color):
colorfunc = color
else:
colorfunc = lambda t: t * color
for p in vw.pxiterator():
z = vw.xpxcart(p[0]) + vw.ypxcart(p[1]) * 1j
i = 0
while abs(z) < zmax and i < n:
z = f(z)
i += 1
data.putpixel(p, colorfunc(float(i) / n), flip=False)
if PYGAME_PIXEL and p[0] == 0:
pygame.display.flip()
if filename is None:
filename = "julia " + str(n) + " " + str(zmax) + " " + str(int(time()))
return data.save(filename, save)
def mandelbrot(vw=ViewWindow(xmin=-2.3,
xmax=0.7,
ymin=-1.5,
ymax=1.5,
dimx=700,
dimy=701),
n=50,
reflect=True,
color=Color(255, 0, 0),
filename=None,
save=True):
data = PlotData(vw)
color0 = color
if callable(color):
colorfunc = color
else:
colorfunc = lambda t: t * color0
for p in vw.pxiterator():
c = vw.xpxcart(p[0]) + vw.ypxcart(p[1]) * 1j
if c.imag > -0.1 or not reflect:
i, z0 = 0, 0
q = (c.real - 0.25)**2 + c.imag**2
if q * (q + (c.real - 0.25)) < c.imag**2 / 4 or 16 * (
(c.real + 1)**2 + c.imag**2) < 1:
data.putpixel(p, colorfunc(1.0), flip=False)
if reflect:
data.putpixel((p[0], vw.ycartpx(-c.imag)),
colorfunc(1.0),
flip=False)
else:
while abs(z0) < 2 and i < n:
z0 = z0 * z0 + c
i += 1
data.putpixel(p, colorfunc(float(i) / n), flip=False)
if reflect:
data.putpixel((p[0], vw.ycartpx(-c.imag)),
colorfunc(float(i) / n),
flip=False)
else:
break
if PYGAME_PIXEL and p[0] == 0:
pygame.display.flip()
if filename is None:
filename = "mandelbrot " + str(n) + " " + str(int(time()))
return data.save(filename, save)
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