Step 1: Materials and equipment
This simple project uses equipment that will be found in nearly all kitchens. I used a slow cooker, but a pot with a lid would work fine too, I imagine. You also need a small bowl and a rubber band. And a styrofoam cup ($2 for 50, but repurpose a used one if you can).
Step 2: What and how
Styrofoam is a brand name for expanded polystyrene (a hydrocarbon polymer blown full of gas). Put a styrofoam cup under high pressure and/or heat and it will shrink dramatically as the gas is driven out. You can do this by putting the cup in a submersible ROV and sending it 1400 m underwater, or much more easily, by popping one in a pressure cooker for half an hour - you'll get a neat miniature coffee cup. It's cute, but not much good for anything (espressos?). The photo above shows how when you heat the coffee cup, it first expands, then shrinks smaller and smaller the longer you leave it. It also gets somewhat distorted, because the plastic gets quite soft. I did these in the slow cooker, but you get a more perfect little cup in a pressure-cooker (see the second photo - it's also faster).
Whether you're making tiny cups or making funky vases of your own design, get the cooker up to heat first (on high). It's also important to cook the cup bain marie style, i.e. inside a bowl that is immersed in water. Otherwise, you'll just melt the cup and make a stinky mess of your cookware.
Step 3: Sculpt a vase
We're going to take advantage of the fact that in the first few minutes in the slow cooker, the cup both softens and expands. This behavior can be manipulated by applying a constant force to some parts of the cup, making it collapse inwards instead.
Take a coffee cup, and put a rubber band around it near the top. Put it in the bowl, replace the lid, and boil for a couple of minutes (watch it, don't time it!). Remove once suitably shape-changed, and take off the rubber band. Done!
Try putting two bands on, or put an odd-shaped object inside to act as a mold (I ran out of used coffee cups, so haven't actually tried the latter). This project is great for experimentation to see what effects you can achieve.
Tip: get the rubber band as tight as possible. Strong, tight bands will create the most interesting effects.
COASTER19 advises that if you have a pressure cooker, you get best results from looser bands, with the cup upside down, and a 7-minute cooking time.
Valaynetine reports that some sorts of polystyrene cup don't change shape at all. The ones I tried - all the same sort - were a soft, relatively bendy type of cup, so that's probably the style to use.
calischs from InstructablesTV made a short video based on this instructable, and cut the rim off then immersed the cup in boiling water with the help of a metal weight. It seemed to work well. Check it out, it's only 46 seconds long!
rojo.balloon made a styrofoam hat from a bowl.
Maurice1985 made an instructable (and made lots more vases than me!) showing how you can fill these with concrete to make a more permanent vase.