I know that I can display an image with the following syntax:

However, is it also possible to directly embed an image into the document to share the Markdown document with the image file directly contained inside it?
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Sign up to join this communityYes, it is possible, using data:
URIs and base64. Terribly inefficient though:

Unfortunately Super User does not allow data:
URIs, it would look like this:
Whether this will work of course depends on whatever you’re using to (pre)view the document. It has to support and allow data:
URIs.
![My image up in the page][1]
followed at some point by [1]: data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAA...
I did some tests and embedding usually works with online markdown editors like dillinger.io, jbt.github.io, stackedit.io, so this topic isn't so black and white as @Spiff wrote above.
This is a screenshot of two base64 blocks inserted by using 1) an internal reference and 2) a common image insertion (see the code below).
1) the referenced base64 block stops being parsed right at the point where 'a new chunk of image' starts, the green part ... So4Z4wxkXa7KukmKul2dDvd ...
2) by passing the block directly we get the whole image
code
1\)![png tester1][pngtester1] 2\)
_1\) the referenced base64 block stops being parsed right at the point where 'a new chunk of image' starts, the green part `... So4Z4wxkXa7KukmKul2dDvd ...`
2\) by passing the block directly we get the whole image_
This was tested with http://tmpvar.com/markdown.html. I don't know how it behaves on github. [The issue](https://github.com/github/markup/issues/270) has been already well discussed.
[pngtester1]:data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHoAAABkCAYAAABJhSQPAAAACXBIWXMAAAsTAAALEwEAmpwYAAADf0lEQVR42u3dW2vTYBzH8eeUPDm0adN2adeddNMpo2ObXoypsDvFd+WbEfRSUUHvxIFOEXG7UEFR5xybulO3tU3XpF4JIiJ43Pw/v+8LKP3nQ54nIaTlC2fOXGKIfAKHANAI0AjQCNAI0AjQCNAI0AjQgEaARoBGgEaARoBGgEaARoBGgAY0AjQCNAI0AjQCNAI0AjQCNKARoBGgEaARoNE/T+EQHL4SwXhsCbnrKWvHU3bdV3rHV3rPlXrPkbqppY5tYXUkVx3JZSo4Z4wxkXa7KukmKul2dDvdd+Mk9ltJ7DeTGNAHXFML+Slnu6slnVkpOfm1og5bttC/8lmp4LwtuGhbzGo40t1kFs7ogyjljNV9ZS9V3OB11Su97XUrWLqJFFtcLEdu9vmRTPSq3+vDHk2oli3k66qXWzie7V8r6AIuxogty+/KbvbxydzActmJcNVNrIYW6uloED0ay4/i9opg64GlH4yHgwe57wL6L/YhtN17k4Xh95HT8z99b0D/xBl891Rx5DDuv4D+AzW1kHMThaFnRzOD//McgP5BT0aD6N5UYYzCLID+Th/ztnPzXFSr+ypDZSZAf3MvPF/LVw/7rRKgf6NtX9nXZsvjW1krS3E+QDPGXgz64e2ZngnKMxoPfXeqMPh0NBimPqex0G3FxfXZythKSZdMmNdI6B1XWlcu9J1uauGYMrNx0OuBpS9f7JsxbW6joD+EtnvlfHXaxFVMABnQpJZrk5GNgN51pDJxTzYKuiM5v3q+epoh2tA3zkUn91zpgpkw9P3xfHWp4pZBTBj6bcXNUnwCBeivatlCXpstY1+mDn1nuucYWIlDv+z3cm+qbi9YCUO3FRe3zkZTICUOPV8L+8BJHLruKevJiWAEnMSh5ybDI6AkDr2VUfbLAR/LNnXo+Vo4AEbi0E0t5IshH9DUoRdHggiEBkA/rOWPg5A49GpBeynHD+KRh148lsUjSOrQKWfs2dHMEPiIQ28ElgM6A6Df9Ho50BkA/arfw20VdeiUM7ZW1EXQEYduaIl3uk2A3sjhQswI6PWc7YHNAOjNwAK0CdBbGUAbAb3r4RUbI6BbWtpgMwC6rbgFNgOgv/z1DyIOLdJuF2wGQNud7j7YDIB24qQNNgOgM42kCTYDoPO7+w2wGQAd1gFtBHRxuw1oE6AL2/stsBkA7cVJB2w/32c7r8DNq/e3jAAAAABJRU5ErkJggg==
This was tested with http://tmpvar.com/markdown.html. I don't know how it behaves on github. The issue has been already well discussed.
No, a Markdown document is just a text file, and text editors (even Markdown-savvy ones) wouldn't know what to do with a blob of binary image data in the middle of a text file.
There are methods like MIME and base64 to encode binary data into a text file in a sense, but most text editors and Markdown-renderers wouldn't know what to do with a MIME encoded document that contains a Markdown text part and a base64 encoded image part.