Floating petals will occasionally appear in your forest. Their spawn rotates with the Leaf Bug, Bark Bug and Dandelion. This means only one of these can occure at once (except for spawns forced by Special Abilities of butterflies).
You will need to try to catch them with one or more of your butterflies by dragging these! It's helpful to use butterflies with the Speed Butterfly Special Ability, like the Cephus Blue Ringlet or the Glasswing.
If you hit a Floating Petal four times, you'll receive one Flutterbuck. For the previous three hits, you will get some honeydew. The amount of honeydew depends on your Flutterpedia Score. For the first hit you will receive 3%, for the second hit you will receive 5,5% and for the third hit you will receive 8% of your score in Honeydew.
The following butterflies are able to create a Floating Petal with their Special Ability every 24 hours: