Embedding image in ipython notebook for distribution
I figured out that replacing the image URL in the  with a base64 URL, similar to the ones found above, can embed an image in a markdown container.
Example markdown:
Are you happy to use an extra code cell to display the image? If so, use this:
from IPython.display import Image
Image(filename="example.png")
The output cell will have the raw image data embedded in the .ipynb file so you can share it and the image will be retained.
Note that the Image class also has a url keyword, but this will only link to the image unless you also specify embed=True (see the documentation for details). So it's safer to use the filename keyword unless you are referring to an image on a remote server.
I'm not sure if there is an easy solution if you require the image to be included in a Markdown cell, i.e. without a separate code cell to generate the embedded image data. You may be able to use the python markdown extension which allows dynamically displaying the contents of Python variables in markdown cells. However, the extension generates the markdown cells dynamically, so in order to retain the output when sharing the notebook you will need to run ipython nbconvert --to notebook original_notebook.ipynb --output preprocessed_notebook using the preprocessor pymdpreprocessor.py as mentioned in the section "Installation". The generated notebook then has the data embedded in the markdown cell as an HTML tag of the form <img src="data:image/png;base64,..."> so you can delete the corresponding code cell from preprocessed_notebook.ipynb. Unfortunately, when I tried this the contents of the <img> tag weren't actually displayed in the browser, so not sure if this is a viable solution. :-/
A different option would be to use the Image class in a code cell to generate the image as above, and then use nbconvert with a custom template to remove code input cells from the notebook. See this thread for details. However, this will strip all code cells from the converted notebook, so it may not be what you want.
The reason why the
<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAnAAAAFgCAYAAAA...
tag doesn't do anything when you put it in a markdown cell is because IPython uses an HTML sanitizer (something called Google Caja) that screens out this type of tag (and many others) before it can be rendered.
The HTML sanitizer in IPython can be completely disabled by adding the following line to your custom.js file (usually located at ~/.ipython/profile_default/static/custom/custom.js):
iPython.security.sanitize_html = function (html) { return html; };
It's not a great solution though, as it does create a security risk, and it doesn't really help that much with distribution.
Postscript:
The ability to render base64 encoded strings as images != obvious security concern, so there should be a way for the Caja people to eventually allow this sort of thing through (although the related feature request ticket was first opened back in 2012, so don't hold your breath).