That is a fungal infection, and doesn't look like one that will be easily cured in an isolated container. This can happen when there is little drainage, and the soil is on the heavy side. It will naturally retain water, and only dry at the top, which will invite infection fairly quickly.
You can try wettable sulfur, but it may be too far spread already. Just make sure that when you are using container, you use a soil with quite a bit of perlite or any material that offers porous, high surface area for aeration.