🌀 The Blue Butterfly is a spirit-like entity that makes its first appearance in the girls bathroom at Blackwell Academy in "Chrysalis" and reappears in an optional ending montage of "Polarized." Throughout the game, there are other depictions of blue butterflies..
Historical
Butterflies are commonly associated with personal growth and transformation as well as transitioning to a new phase (in life), such as the transition from childhood to adulthood. Transition starts in the form of a chrysalis - the title of the first episode. A chrysalis is symbolic of the changes Max undergoes before she matures into a more confident version of herself.

For Christians, butterflies are a symbol of rebirth. ❀

In Japanese folklore, a white butterfly represents the soul of a deceased loved one.. A famous Chinese love story, the Butterfly Lovers, tells of two butterflies that rose from a grave after a woman threw herself into it to be with her deceased lover. This tale is famous in East Asia where butterflies are thought of as a symbol of immortality, long life, and romanticism. Butterflies can be seen as a sign of comfort at funerals or as a guide for those having difficulties with life decisions.

In Ancient Greece, the butterfly was associated with the word psyche, which meant soul. Many other ancient cultures also thought of butterflies as representing human souls - souls of the dead.[4] They carry many meanings to many different cultures around the world, but the themes mentioned above seem to be the most common.

Butterflies are also a universal symbol of beauty. 💙🦋⏳

The Butterfly Effect
The Butterfly Effect is addressed throughout Life Is Strange, because even when Max uses her powers to alter what she sees as the smallest of things, this can have serious consequences later on. The butterfly effect comes under a branch of mathematics called Chaos Theory which deals with the unpredictability of events, and the term itself originates from a scientific paper written in 1972 by a meteorologist called Edward Lorenz entitled Predictability: Does the Flap of a Butterfly's Wings in Brazil set off a Tornado in Texas?.

It is interesting that the events of Life is Strange begin with the appearance of a butterfly at the beginning and end with a tornado, perfectly mirroring Lorenz's theory. Max also sees the tornado as a culmination of all the changes she has made to the timeline: "This is my storm. I caused this... I caused all of this. I changed fate and destiny so much that... I actually did alter the course of everything. And all I really created was just death and destruction!"

The notion of a small change causing significant damage in the future is also addressed in a work of fiction by Ray Bradbury called A Sound of Thunder. In this story, time travel is possible, and the wealthy can pay to travel back in time to hunt extinct species. A hunter, a guide, and an assistant travel back to the Late Cretaceous period to hunt and kill a Tyrannosaurus rex. The hunter, Eckels, is warned in advance to stick to the designated path, but he panics upon seeing the T-Rex and deviates. When they return to the future, it has changed, and Eckels examines his boots to discover a crushed butterfly from the past. It is the premature death of such a small thing that is thought to have brought greater consequences on the future.

This action will have consequences- 🦋
After a choice is made in Life is Strange, an animated sketch of a butterfly appears with a warning in the top left corner of the screen to remind the player that "This action will have consequences." This serves to remind the player that this action creates a butterfly effect and the results will be seen later on.
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The blue butterfly resembles a neotropical butterfly from the genus Morpho - more specifically, the species Morpho didius. These can be found in South America, Mexico, and Central America. It is also similar to (but less so) a Ulysses Butterfly (Papilio ulysses) which is commonly found in Australia, Indonesia, Papua New Guinea and the Solomon Islands.
The first episode's title, "Chrysalis", is the name of the pupa life stage of butterflies, and so refers to a metamorphosis undergone by butterflies. Figuratively, it refers to the beginning of Max's journey and coming-of-age story.
On page 8 or Max's diary, in reference to the butterfly analogy, she writes: "At least I'm trying to climb out of my cocoon. I shouldn't expect my life to completely change after a few weeks of Blackwell Academy."
The blue butterfly is believed to be Chloe's spirit. This idea is reinforced by a drawing in Max's journal during her nightmare. The drawing is a butterfly with Chloe's head, and the texture file for this drawing in the game files is named Spirit_animal_Chloe.
The cover art for Breton's album "War Room Stories" - from which the song "Got Well Soon" is featured at the End of the World Party - displays a blue butterfly.˙📷⋆.ೃ࿔*:･