Shulou(Shulou.com)06/02 Report--

In this issue, the editor will bring you about how python draws cool dynamic Julia sets. The article is rich in content and analyzes and narrates it from a professional point of view. I hope you can get something after reading this article.

Preface

This Julia is not the other Julia, which refers to the set of complex z z z for a complex c c c such that the iterative formula f (z) = Z2QuC f (z) = z ^ 2 + c f (z) = Z2Crc converges. For example, when cedar 0 cis 0 cv 0, then its convergence interval is z 2.

M] = I # record the divergence velocity of the divergence point z = Zhonz + c print ("time:", time.time ()-t) return outz1 = genZ (- 2lemently1.5) mBrot = getJulia (Z1LZ) 50) plt.imshow (mBrot.get (), cmap=plt.cm.jet) plt.show ()

If you are interested in its generation process, you can observe how the image changes as the number of iterations increases.

The code is as follows.

From matplotlib import animationfig = plt.figure () fig.subplots_adjust (top=1, bottom=0, left=0, right=1) ax = plt.subplot () def getJulias Cp.abs (z) c = cp.zeros_like (z) + c J = [] for i in range (n): Z = Zhonz + c absz = cp.abs (z) z [absz > m] = 0 # zero c [absz > m] = 0 out [absz > m] = I # record the divergence velocity of the divergence point Im = ax.imshow (out.get () Cmap=plt.cm.jet, animated=True) ax.set_axis_off () J.append ([im]) return JN = 75 # number of iterations Z1 = genZ (- 2 interval=50 1.5) 1000pc003) J = getJulias (Z1 interval=50, blit=True,repeat_delay=1000 N) ani = animation.ArtistAnimation (fig, J, interval=50, blit=True,repeat_delay=1000) plt.show () ani.save ('julias.gif',writer='imagemagick') infinite scaling

The fractal feature of the Mandelbrot set means that the image we generate can be magnified infinitely, but due to the influence of the rasterized size, manual magnification will not change its true size.

In order to take care of the look and feel, the zoom center is taken as the center of the image, so the genZ function is modified. If (- 0.75) is selected as the zoom center, the change is as follows

The code is

From matplotlib import animation# generates z coordinates xy=np.array ([xc,yc]) as the starting point, and # nxy=np.array ([nx,ny]) as the number of points Delta is the distance from the point def genZbyCenter (xy,nxy,delta): X0Magne y0 = xy-np.array (nxy) * delta/2 return genZ) mBrots = [] xy = [- 0.75 Lindlle 0.2] nxy = [1000L1000] delta0 = 0.003 # initial width fig = plt.figure () fig.subplots_adjust (top=1, bottom=0, left=0, right=1) ax = plt.subplot for n in range (50): Z1 = genZbyCenter (xy,nxy) 1.1 ax.set_axis_off * (- n) * delta0) out = getJulia (Z1Powerz1jing40) im = ax.imshow (out.get (), cmap=plt.cm.jet, animated=True) ax.set_axis_off () mBrots.append ([im]) ani = animation.ArtistAnimation (fig, mBrots, interval=50, blit=True) plt.show () ani.save ('zoom.gif',writer='imagemagick') Julia set

If you change the value of c, you will get a changing Julia set, for example, select a straight line below

Yellowx yellowx yellowx

The above Julia set has the effect shown in the figure

The code is

Z1 = genZ (- 2) fig.subplots_adjust (top=1, bottom=0, left=0, right=1) ax = plt.subplot () mBrots = [] for x in np.arange (0.5 out): C = x + x, 1j out = getJulia (z1Power40) im = ax.imshow (out.get), cmap=plt.cm.jet Animated=True) ax.set_axis_off () mBrots.append ([im]) ani = animation.ArtistAnimation (fig, mBrots, interval=50) plt.show () ani.save ('julia.gif',writer='imagemagick') this is how python draws cool dynamic Julia sets that Xiaobian shared with you. If you happen to have similar doubts, you might as well refer to the above analysis to understand. If you want to know more about it, you are welcome to follow the industry information channel.

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