Translation of "Spontaneously" in Spanish

Babies learn their native languages naturally and spontaneously

aprenden su lengua materna natural y espontáneamente

My grandmother has a lot of vegetation that grows spontaneously.

Mi abuela tiene mucha vegetación que crece espontáneamente.

Things alter for the worse spontaneously, if they be not altered for the better designedly.

Las cosas cambian para peor espontáneamente, si no se cambian para mejor deliberadamente.