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()


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