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 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 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 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 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 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 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 slopefield(f, vw=ViewWindow(), spread=20, color=0x0000FF, filename="slopefield" + str(int(time())), save=True): tmp = vw.thick vw.thick = 0 data = PlotData(vw) cartspreadx = vw.xpxcart(spread) - vw.xpxcart(0) cartspready = vw.ypxcart(spread) - vw.ypxcart(0) for i in range(vw.dimx): for j in range(vw.dimy): if i % spread == 0 and j % spread == 0: theta = atan(f(*vw.xpxcart((i, j)))) data.line((vw.xpxcart(i) + cartspreadx * cos(theta) / 4, vw.ypxcart(j) - cartspready * sin(theta) / 4), (vw.xpxcart(i) - cartspreadx * cos(theta) / 4, vw.ypxcart(j) + cartspready * sin(theta) / 4), color) vw.thick = tmp 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 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 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 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 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 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 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 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 rk4(f, initlist, vw=ViewWindow(), h=.001, colorlist=None, sf=False, sfspread=20, sfcolor=0x0000FF, filename="rk4" + str(int(time())), save=True): data = PlotData(vw) if sf: data.data = list( slopefield(f, vw, sfspread, sfcolor, save=False).getdata()) if colorlist is None: colorlist = Color.colors(len(initlist)) for i in range(len(initlist)): c = colorlist[i] for h1 in [h, -h]: x0, y0 = initlist[i] while vw.xmin < x0 < vw.xmax: if colorlist == "rainbow": c = Color.rbow( 2 * pi * (x0 - vw.xmin) / (vw.xmax - vw.xmin), 2) k1 = f(x0, y0) k2 = f(x0 + h1 / 2, y0 + h1 * k1 / 2) k3 = f(x0 + h1 / 2, y0 + h1 * k2 / 2) k4 = f(x0 + h1, y0 + h1 * k3) x1, y1 = x0 + h1, y0 + (h1 / 6) * (k1 + 2 * k2 + 2 * k3 + k4) data.line((x0, y0), (x1, y1), c) x0, y0 = x1, y1 return data.save(filename, save)
def slopefield(f, vw=ViewWindow(), spread=20, color=0x0000FF, filename="slopefield" + str(int(time())), save=True): tmp = vw.thick vw.thick = 0 data = PlotData(vw) cartspreadx = vw.xpxcart(spread) - vw.xpxcart(0) cartspready = vw.ypxcart(spread) - vw.ypxcart(0) for i in range(vw.dimx): for j in range(vw.dimy): if i % spread == 0 and j % spread == 0: theta = atan(f(*vw.xpxcart((i, j)))) data.line((vw.xpxcart(i) + cartspreadx * cos(theta) / 4, vw.ypxcart(j) - cartspready * sin(theta) / 4), (vw.xpxcart(i) - cartspreadx * cos(theta) / 4, vw.ypxcart(j) + cartspready * sin(theta) / 4), color) vw.thick = tmp return data.save(filename, save)
def rk4(f, initlist, vw=ViewWindow(), h=.001, colorlist=None, sf=False, sfspread=20, sfcolor=0x0000FF, filename="rk4" + str(int(time())), save=True): data = PlotData(vw) if sf: data.data = list(slopefield(f, vw, sfspread, sfcolor, save=False).getdata()) if colorlist is None: colorlist = Color.colors(len(initlist)) for i in range(len(initlist)): c = colorlist[i] for h1 in [h, -h]: x0, y0 = initlist[i] while vw.xmin < x0 < vw.xmax: if colorlist == "rainbow": c = Color.rbow(2 * pi * (x0 - vw.xmin) / (vw.xmax - vw.xmin), 2) k1 = f(x0, y0) k2 = f(x0 + h1 / 2, y0 + h1 * k1 / 2) k3 = f(x0 + h1 / 2, y0 + h1 * k2 / 2) k4 = f(x0 + h1, y0 + h1 * k3) x1, y1 = x0 + h1, y0 + (h1 / 6) * (k1 + 2 * k2 + 2 * k3 + k4) data.line((x0, y0), (x1, y1), c) x0, y0 = x1, y1 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 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 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 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 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 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 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 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 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 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 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