The wasabi plant (Wasabia japonica) is native to Japan, where it grows in mountain rivers. However, it is a plant that also adapts well to living, both in a pot, or in the garden, where it can last for several years.
Getting a log to grate seems complicated (although not impossible!). Very likely you will be able to harvest leaves and flowers, which you can enjoy in salads, tempura, blanched, or simply as decoration.
With any luck, the plant will put out suckers, which you can transplant and grow your wasabi garden at home!