The episode name may be a reference to a 2004 American Science fiction psychological thriller film, The Butterfly Effect. It could also be named after the Butterfly Effect in the Chaos Theory, as shown by the wind produced by the butterfly.
Matilda is admiring a butterfly. The pigs have the idea to create a replica butterfly to distract Matilda from the nest...
On an extremely hot day, Matilda was cooling herself and the eggs down in the heat using a piece of white cloth. Her attention was caught by a butterfly fluttering around her. It briefly spun, which caused Matilda to imitate that. Then the butterfly began to cool her down, using its wings as fans. Satisfied with this, Matilda waved goodbye to the butterfly as it left, and continued to cool the eggs.
In a bush, three pigs in a stack, with the one at the bottom sweating (Corporal Pig on top) spied on Matilda. Seeing her get distracted by the butterfly, Corporal Pig got an idea and decided to make a fake butterfly to distract her. Corporal Pig produced a fishing rod and swiftly crafted a butterfly made of sticks, leaves, and paint. The "butterfly" went over to Matilda, who admired the butterfly again. However, she became hot doing this, and as a desperate attempt to keep Matilda's attention, one of the three pigs vigorously shook the rod, making the butterfly go through a large amount of pressure to fan Matilda.
Unfortunately, this caused the butterfly to fall apart. One of its wings (leaves) fell off, which alarmed Matilda and quickly placed it back on again. However, the same happened with the other wings and the head, causing Matilda to faint. The pigs, satisfied with the reaction, came over to steal the eggs. The real butterfly then flew back in the attempt to revive Matilda by fanning her with its wings again. This made Corporal Pig bring out a fly swat in the attempt to kill the butterfly. However, it was too fast and landed on a minion pig's head. Corporal Pig swatted at the pig, just as the butterfly flew out of the way. This caused the pig to scream, catching Matilda's attention. She shadowed them just as Corporal Pig brought the eggs to her. However, this action just made Matilda more angry. Putting down the eggs, Matilda scared them off, causing them to run away in fear, but were still attacked.
The real butterfly came over to land on Matilda to relax in a cool breeze. However, when it stopped, Matilda yelled. It was revealed that the pigs, severely injured, were hanging onto a tree branch in a stack, with Corporal Pig on top. They were fanning Matilda with large leaves, similar to the butterfly. Matilda's yells caused them to speed up fanning.
In the credits, they could still be heard fanning Matilda and the real butterfly even faster as she yelled more at them.