Mushrooms are actually the reproductive system of the organism mycelium, so technically this project is about growing mycelium into any form you want, in this case an architectural model.
Since mycelium grows by consuming carbon rich materials like wood chips, straw, cotton, etc, the shape that it will grow into can be organized by stuffing a formwork with mycelium food.
Disclaimer: If mishandled, pressure cookers can be dangerous. Additionally, in letting things decompose there is the a potential for unwanted bacteria or fungus growth. Attempt at your own risk!
Step 1: Get Mycelium
There are a few different ways to get mycelium. Of course it grows naturally in the wild and you can grow your own through propagating spoors or through tissue samples. Both of these methods are kind of involved, so I'm not going to cover them in this instructable.
An easier option is to buy ready grown mycelium online, for example:
You can also sometimes find "spent" mycelium blocks at mushroom farms for free and revive them by breaking them up and adding new substrate. Because these blocks have been growing for a while there is more risk of bacterial contamination, nevertheless, I've had a lot of success with this method. Even the mycelium in the block with the shriveled up mushrooms has the potential of being revived, but the fresher the better.
If you want your model to grow really fast and you've purchased a fresh block, you can skip the next two steps and just break up your block and pack it around your form. However, if you're recycling blocks or you want to get the most out of the mycelium you've purchased you can add more substrate.
Step 2: Sterilize Your Substrate
While I've used a lot of substrates including wood chips and coffee grounds, the carbon based mycelium food or "substrate" I usually use is straw. Straw is a waste product available very affordably in bale form at feed stores and race tracks. Chop some straw into small pieces, cover it with water and sterilize it in a pressure cooker for an hour. Once the pressure cooker is cool enough to open, wash your hands, clean all work surfaces and implements with rubbing alcohol, and drain the straw in a clean strainer. Cool to 75 degrees and use immediately to reduce the potential for bacteria exposure.
Step 3: Inoculate the Substrate With Mycelium
Wash your hands again and break up the mycelium block you've purchased or scavenged into small pieces. You don't need a whole block for such as small project, so you can save the rest of the block for another purpose. Mix these pieces in with your chopped straw and try to distribute them evenly throughout the mix.
Step 4: Design Your Formwork
The formwork can really be anything in any form that you want. I've used plastic, plexiglass, 3d prints, etc. The mycelium will grow into, or begin to consume organic materials such as wood, which can be useful for some applications, but not very convenient if you're trying to extract your formwork later. For the formwork above I wrapped the pieces of plywood with clear tape to prevent this from happing.
Step 5: Place the Substrate
Pack the substrate and mycelium around the form. The tighter it's packed the smoother the final product will be. Mycelium takes on whatever form and surface you present it with, so packing the substrate against smooth materials such as plexiglass or plastic will result in a smooth finish.
Step 6: Seal It Up
I use a plastic bag welder to seal the model up completely. Mycelium needs oxygen to grow since it consumes oxygen and expels CO2, like us. You can buy special bags for growing mycelium that come with a welded in filter strip that allows gas exchange, but does not allow bacteria to get in. I find that I'm growing the models so rapidly that keeping bacteria out is not a high priority and I just leave a very tiny hole for gas exchange. If the bag is sealed up with enough moisture you won't need to mist it during the growth stage. Store the model in a cool (55-75 degrees) dark place to discourage bacterial growth.
Step 7: Let It Grow
I usually let the mycelium grow for a week or a week and a half. If you let it grow too long it will eventually fruit mushrooms. Once this has happened there are potentially mushroom spoor on your model and in theory, given the right conditions mushrooms could start growing again. If you start to see green or black spots, your substrate has become contaminated with bacteria and should probably be composted.
Step 8: Remove Form
Once the model looks sufficiently covered in a white mat, you can halt the growing process. At this point you don't need to worry about contamination anymore, so you can just cut open the plastic bag and remove the form. Because the mycelium is moist it is still pretty fragile, so remove the form very carefully.
Step 9: Bake Your Model
Preheat your oven to 200 degrees F and bake your model for 45 minutes. This will effectively kill the mycelium and prevent any further growth. It will also dry out your model create a sturdy final product.
Step 10: Add Scalies
Add some architectural scalies (scaled figures) and you're done!