Answer: Alyssum is an annual plant, so it won't come back. Annuals are plants whose life cycle (vegetative growth, bloom, seed set) is completed in a single growing season. The plant dies at the end of the cycle and a new generation begins with seed germination. However, it does self-sow readily, so if you allow the seeds to dry and fall off, you will probably have more plants sprouting. Or, you can collect the seed to sow elsewhere. The seeds are quite tiny.
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