Python for Quickiebrot

Here is the script for the post Quickiebrot I. It draws the Mandelbrot set interactively. You can click on the image to recenter, and slide the "zoom" slider.

It is so long because I copied a vertically modified slider from the internet.

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# Vertical Slider Modification # from here: http://www.tagwith.com/question_718868_add-a-vertical-slider-with-matplotlib # and here: http://stackoverflow.com/questions/25934279/add-a-vertical-slider-with-matplotlib from matplotlib.widgets import AxesWidget class VertSlider(AxesWidget): """ A slider representing a floating point range The following attributes are defined *ax* : the slider :class:`matplotlib.axes.Axes` instance *val* : the current slider value *vline* : a :class:`matplotlib.lines.Line2D` instance representing the initial value of the slider *poly* : A :class:`matplotlib.patches.Polygon` instance which is the slider knob *valfmt* : the format string for formatting the slider text *label* : a :class:`matplotlib.text.Text` instance for the slider label *closedmin* : whether the slider is closed on the minimum *closedmax* : whether the slider is closed on the maximum *slidermin* : another slider - if not *None*, this slider must be greater than *slidermin* *slidermax* : another slider - if not *None*, this slider must be less than *slidermax* *dragging* : allow for mouse dragging on slider Call :meth:`on_changed` to connect to the slider event """ def __init__(self, ax, label, valmin, valmax, valinit=0.5, valfmt='%1.2f', closedmin=True, closedmax=True, slidermin=None, slidermax=None, dragging=True, **kwargs): """ Create a slider from *valmin* to *valmax* in axes *ax* *valinit* The slider initial position *label* The slider label *valfmt* Used to format the slider value *closedmin* and *closedmax* Indicate whether the slider interval is closed *slidermin* and *slidermax* Used to constrain the value of this slider to the values of other sliders. additional kwargs are passed on to ``self.poly`` which is the :class:`matplotlib.patches.Rectangle` which draws the slider knob. See the :class:`matplotlib.patches.Rectangle` documentation valid property names (e.g., *facecolor*, *edgecolor*, *alpha*, ...) """ AxesWidget.__init__(self, ax) self.valmin = valmin self.valmax = valmax self.val = valinit self.valinit = valinit self.poly = ax.axhspan(valmin, valinit, 0, 1, **kwargs) self.vline = ax.axhline(valinit, 0, 1, color='r', lw=1) self.valfmt = valfmt ax.set_xticks([]) ax.set_ylim((valmin, valmax)) ax.set_yticks([]) ax.set_navigate(False) self.connect_event('button_press_event', self._update) self.connect_event('button_release_event', self._update) if dragging: self.connect_event('motion_notify_event', self._update) self.label = ax.text(0.5, 1.03, label, transform=ax.transAxes, verticalalignment='center', horizontalalignment='center') self.valtext = ax.text(0.5, -0.03, valfmt % valinit, transform=ax.transAxes, verticalalignment='center', horizontalalignment='center') self.cnt = 0 self.observers = {} self.closedmin = closedmin self.closedmax = closedmax self.slidermin = slidermin self.slidermax = slidermax self.drag_active = False def _update(self, event): """update the slider position""" if self.ignore(event): return if event.button != 1: return if event.name == 'button_press_event' and event.inaxes == self.ax: self.drag_active = True event.canvas.grab_mouse(self.ax) if not self.drag_active: return elif ((event.name == 'button_release_event') or (event.name == 'button_press_event' and event.inaxes != self.ax)): self.drag_active = False event.canvas.release_mouse(self.ax) return val = event.ydata if val <= self.valmin: if not self.closedmin: return val = self.valmin elif val >= self.valmax: if not self.closedmax: return val = self.valmax if self.slidermin is not None and val <= self.slidermin.val: if not self.closedmin: return val = self.slidermin.val if self.slidermax is not None and val >= self.slidermax.val: if not self.closedmax: return val = self.slidermax.val self.set_val(val) def set_val(self, val): xy = self.poly.xy xy[1] = 0, val xy[2] = 1, val self.poly.xy = xy self.valtext.set_text(self.valfmt % val) if self.drawon: self.ax.figure.canvas.draw() self.val = val if not self.eventson: return for cid, func in self.observers.iteritems(): func(val) def on_changed(self, func): """ When the slider value is changed, call *func* with the new slider position A connection id is returned which can be used to disconnect """ cid = self.cnt self.observers[cid] = func self.cnt += 1 return cid def disconnect(self, cid): """remove the observer with connection id *cid*""" try: del self.observers[cid] except KeyError: pass def reset(self): """reset the slider to the initial value if needed""" if (self.val != self.valinit): self.set_val(self.valinit) # OK done with the vertical slider modification. Here is the real script! import numpy as np import matplotlib.pyplot as plt from matplotlib.widgets import Cursor def get_setup(cx0=-1.0, cy0=0.0, half_width=2.0): global NSTEP, npcx, npcy hwx = half_width hwy = (9./16.) * half_width # 16:9 cx1, cx2 = cx0 - hwx, cx0 + hwx # -3.0, 1.0 # 4 = 16 / 4 cy1, cy2 = cy0 - hwy, cy0 + hwy # -1.125, 1.125 # 2.25 = 9 / 4 #npcx, npcy = 1280/2, 720/2 npcx, npcy = 1280, 720 cxt = np.linspace(cx1, cx2, npcx) cyt = np.linspace(cy1, cy2, npcy) # so cx = cx1 + (ipix/npcx)*(cx2-cx1) cX, cY = np.meshgrid(cxt, cyt) c = cX + j*cY NSTEP = 100 z = np.zeros((NSTEP, npcy, npcx), dtype = 'complex') z[0] = np.complex(0, 0) nout = np.zeros((npcy, npcx)) return z, nout, c, cx1, cx2, cy1, cy2 def f4(z, c): return z**2 + c def go(): global NSTEP print("confirm 1 c[0,0] = ", c[0,0]) for k in range(1, NSTEP): z[k] = f4(z[k-1], c) out = abs(z[k]) > 2. z[k, out] = np.nan nout[out] = k j = np.complex(0, 1) z, nout, c, cx1, cx2, cy1, cy2 = get_setup() go() fig, ax = plt.subplots() plt.subplots_adjust(left=0.2, bottom=0.05, top=0.95, right=0.95) axcolor = 'lightgoldenrodyellow' #slider ax_zoom = plt.axes([0.08, 0.2, 0.04, 0.6], axisbg=axcolor) # added zoomval = 0.0 zoom = 10.**zoomval zoomvalmax = 5 szoom = VertSlider(ax_zoom, 'zoom', 0, zoomvalmax, valinit=zoomval) # added VertSlider icount = 1000 def p(): global icount zac = np.abs(z[-1]) uhoh = np.isnan(zac) A = 2. * zac A[uhoh] = nout[uhoh] icount += 1 plt.imsave('wowow'+str(icount), A) ax.imshow(A) p() def updatezoom(val): global z, nout, c, cx1, cx2, cy1, cy2 global zoom #global icount zoomval = (max(0.0, min(zoomvalmax,szoom.val))) zoom = 10**zoomval cx, cy = 0.5*(cx1 + cx2), 0.5*(cy1 + cy2) hwz = 2.0 / zoom z, nout, c, cx1, cx2, cy1, cy2 = get_setup(cx0=cx, cy0=cy, half_width=hwz) go() p() #icount += 1 #plt.savefig('wow'+str(icount)) plt.draw() #icount = 1 szoom.on_changed(updatezoom) def onclick(event): global z, nout, c, cx1, cx2, cy1, cy2 global npcx, npcy #npcx, npcy = 1280, 720 if event.x > 132: ipx, ipy = event.xdata, event.ydata cx = cx1 + (float(ipx)/float(npcx)) * (cx2-cx1) cy = cy1 + (float(ipy)/float(npcy)) * (cy2-cy1) print " hey! ", event.button, event.x, event.y print ipx, ipy, cx, cy hwz = 2.0 / zoom z, nout, c, cx1, cx2, cy1, cy2 = get_setup(cx0=cx, cy0=cy, half_width=hwz) go() p() plt.draw() # so cx = cx1 + (ipix/npcx)*(cx2-cx1) cid = fig.canvas.mpl_connect('button_press_event', onclick) plt.savefig("wowza") plt.show()