Speculation with portals
Let's discuss portals and what they will do in specific scenarios.
For example, let's say that portals withstand motion (This in actually self-explanatory if you take molecular vibration into account), let's also say you can place portals on organic material (The definition of "organic" is that the molecular formula includes carbon, with the exception of carbonate and carbon gas) If you were to place portal A on a wall in front of you, and portal B on your chest. If you now were to run straight into portal A facing forwards, what would happen?
Picture of scenario:
You are also assuming that you can somehow create portals of different size, yet have them operate normally, which means that the linearity of space becomes screwed around the portal rims.
a portal inside a portal would create a space and time paradox and the whole of existance would go 'pop'
Yes, a portal inside a portal would make everything die instantly.
Let's tihnk of the universe as a giant piece of paper.
When you place a portal link, you're essentially folding this piece of paper to connect with the other point.
____________
______
______
So, if you were to place a portal inside a portal, you'd essentially be doing this:
.
The paper would fold around itself so much that it becomes an invisible blip of existance.
Say NO to ASCII drawings!
Say YES to MS paint (or any other program that is more powerful such as photoshop for the gimp for those who are poor)
Let's tihnk of the universe as a giant piece of paper.
When you place a portal link, you're essentially folding this piece of paper to connect with the other point.
____________
______
______
So, if you were to place a portal inside a portal, you'd essentially be doing this:
.
The paper would fold around itself so much that it becomes an invisible blip of existance.
Yes, essentially the universe would disappear up it's own arse.
Does anyone else have any scenarios?
Portals of different sizes would also be very tricky to get aound.
Think about this - A potals is a wormhole that is 0mm thick. A wormhole can have different sized entrances and exits because it is relatively long inside and stretches and squashes anything that enters, a portal on the other hand has entrances and exits that are actually touching meaning if one was smaller than the other the space on the other side would be enlarged or shrunk and anythign that wen't through would stay the wrong size(if you kept going from big portal to small portal you would end up microscopic...).
portals on curved surfaces? anyone got any thoughts whilst I'm out for the evening?
I have long been thinking of one...
If there are 2 blue portals (maybe due to some mailfunction in the device)
that lead to the same one red portal, what would happen if somebodysomething enters the red one? Duplication?
Let's tihnk of the universe as a giant piece of paper.
When you place a portal link, you're essentially folding this piece of paper to connect with the other point.
(ASCII art cut to save space)
The paper would fold around itself so much that it becomes an invisible blip of existance.
This is a really geeky hypothetical discussion of an imaginary technology, but I'm up for it. 
I totally disagree with the assessment above.
First, the paper analogy is badly flawed. You're not "essentially folding this piece of paper" when you place a portal link. If that were true, we would be able to observe the entire world geometry deform when we placed portals. That clearly doesn't happen. So the argument that placing a portal inside a portal would infinitely deform space is invalid.
Second, portals themselves have no mass, no substance. In a certain way of thinking, they have no physical properties of their own; rather, they erase the physical properties of the surfaces on which they are placed, like its solidity and its position in spacetime. (This is why cameras fall off the walls when you place a portal behind them. The solidity/presence of the wall is negated by the portals.) So if portals have no material existence, and by definition portals must be placed on solid objects, you could never place a portal in a portal.
Third, portals disappear whenever the surface they're on moves or rotates. This means it's impossible to place a portal on a moveable surface in order to push one portal into/through another.
Basically what I'm saying is that the question doesn't make sense. "What would happen if you place a portal in a portal?" is impossible according to the definition of portals. Their observed behavior confirms and reinforces this impossibility.
(Sorry to be a killjoy. )