If you simply can't be satisfied with the occasional chance appearance of a butterfly in your garden, you might consider planting a butterfly garden... a landscape intended to attract butterflies.
Louisiana is on the migration route for the monarch butterfly. This butterfly overwinters in Mexico, migrates to the northern United States in spring and summer, and then travels back down to Mexico in the fall. Many gardeners plant milkweed in their gardens to provide for the monarch butterflies.
To properly plant a butterfly garden, you need a general understanding of the lifecycle of butterflies.
Note that butterfly caterpillrs will feed ferociously on the leaves of many plants. Each type of butterfly caterpillar will only feed on a specific kind of plant and the adult mother butterfly will only lay eggs on the specific type of plant that will properly nourish her offspring.