On my street lots of trees have a big burl at the base.
Is there a technique to "encourage" trees to develop it?
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There's no real consistent way to encourage burls to grow on trees. Burls are a reaction to various kinds of infections and possibly damage. They can weaken a tree and raise it's susceptibility to more deadly infections. There's no way to purposefully try and create or encourage their growth and there's at least some debate about the exact circumstances that lead to burls being created.
Basal burls on Redwoods are a little different from other burls - they used to be called lignotubers, and are a natural reproductive structure for these trees. It's thought that this type of basal burl is genetically controlled, whereas other swellings which may occur on other parts, or at the base, of trees are an environmental response, maybe to fungal or bacterial infection. This type of burl may also be known as a gall or, sometimes, a tumour - an example would be crown gall, which affects many species of tree.
Unless your tree is a redwood, then any other gall or burl either happens or it doesn't.
The traditional method that probably caused what you are seeing is to run into the tree with a lawnmower a lot - once every week or two throughout the growing season.
Note that this is not a good idea (tree health-wise), but it is a common cause of damage near ground level in trees in domesticated areas.