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Just like bacteria, fungi need a food source, moisture and warmth to grow well. In addition, most need oxygen to grow.
Compost bins are ideal for fungal growth as they provide the right conditions for the decomposition (break down) of plant material. Fungi, and also bacteria, act as decomposers to break down the plant material put in there.
Most fungi flourish is moist and warm conditions, including on parts of our bodies and in our houses. Fungi that thrive on our bodies include the fungi that cause nail fungal infections, athlete's foot and thrush. Houses and rooms of houses that are damp and poorly ventilated often get condensation on the windows and dampness on curtains, walls, clothes and wooden fittings. If the rooms are warm enough (through heating) then moulds have the ideal conditions to grow and reproduce. Some of these moulds can make us quite ill because some fungi excrete toxins (see the page on fungal excretion).
Fungi can be cultured and grow well on agar plates. The agar provides the food source and moisture, and the incubator provides the warmth. Any fungi that land on a suitable food source can start to grow and reproduce quite rapidly on the food source. Fungal colonies look furry/fuzzy/fluffy due to the presence of hyphae. See the pages on culturing microbes and fungal reproduction for more information.