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    <p>You can calculate a histogram (2D) of the x, y values using numpy's <a href="http://docs.scipy.org/doc/numpy/reference/generated/numpy.histogram2d.html" rel="nofollow noreferrer">histogram2d</a> method. Then you plot the array that is true for all non-zero bins and false for all zero bins. You can control the resolution of the histogram using the <code>bins</code> parameter. This method returns a tuple of 3 arrays: the 2D histogram and two 1D arrays corresponding the bin steps along each 'edge' (x then y). You can control the step values using the <code>range</code> parameter.</p> <p>For example:</p> <pre><code>import matplotlib.pyplot as plt import numpy as np np.random.seed(101) x = np.random.normal(0,1,10000) y = np.random.normal(0,1,10000) hist,xedge,yedge= np.histogram2d(x,y,bins=100,range=[[-4,4],[-4,4]]) plt.imshow(hist==0, origin='lower', cmap=plt.gray(), extent=[xedge[0],xedge[-1],yedge[0],yedge[-1]]) plt.savefig('hist2d.png') plt.show() </code></pre> <p>This results in:</p> <p><img src="https://i.stack.imgur.com/HjK0b.png" alt="enter image description here"></p> <p>The black points show where you have any data, the white points are where there is no data. The histogram is presented using the <code>imshow</code> method, which is used to plot images or matrices. By default it set's the origin to the top left, so you will either want to change the parameter <code>origin='lower'</code>, or you want to appropriately adjust the <code>extent</code> parameter, which controls the range values: [intial x, final x, initial y, final y]. You can control the color scheme by adjusting the <a href="http://matplotlib.sourceforge.net/api/pyplot_api.html#matplotlib.pyplot.colormaps" rel="nofollow noreferrer">color map</a>.</p> <p>As @joaquin mentions in the comments, you can also simply plot <code>imshow(hist)</code> to see the full range of values (heatmap), rather than 0 or 1.</p>
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    1. CO+1 You could have a heatmap just doing `plt.imshow(hist)`. Maybe the OP likes it better as it gives sense of density at each point not just yes/no (and it is nicer)
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    2. CO+1 As a side note, though, `histogram2d` is inefficient for large numbers of points. You'll run into memory problems if you use it for more than a few tens of thousands of points. It becomes much faster to either iterate or trick `scipy.sparse.coo_matrix` into doing it for you.
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    3. COWoops, partially scratch my previous comment, it's quite fast if you have a small number of bins, even with a large number of points. It becomes less efficient than other solutions when you have both a large number of bins and a large number of points. Also, my memory of it being inefficient was based on a much earlier version. It's still reasonably efficient even in those cases with recent versions of numpy.
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