Place the rice and water into the rice cooker (or pot). Cook according to the instructions on the packet.
Once done, season with the rice vinegar, sugar and salt; mix through and set aside to cool.
Slice the avocado and capsicum into strips.
Divide the cooled rice into 4 portions. Place one sheet of nori, shiny side down, on a sushi mat.
Moisten your fingers with some water to prevent the rice from sticking to them, then spread the rice evenly over the nori sheet. Leave about one inch at the top without rice.
With the exposed end of the nori facing away from you, spread ¼ of each of the vegetables down the end closest to you, a bit in from the edge of the rice. Add vegan mayonnaise if desired.
Next, roll the sushi away from you. You need to grip the mat firmly but not squash the sushi. Once rolled, seal the end with water.
Now cut the sushi into 8 pieces.
Repeat this process for the rest of the rolls.
Serve immediately with soy sauce, pickled ginger and wasabi.