Iterative Functions

Iteration means doing it again. A magic box changes a number and gives you a new one. Put that new number right back in! After thousands of times, a secret shape appears. This is how computers draw mountains in video games. Our daily habits eventually shape who we are.

Our daily habits eventually shape who we are. Put yourself into the box, come out changed, go back in. Repeat until the secret shape appears.

Repeated application of f(x) can produce fixed points, limit cycles, or chaotic attractors. Complexity arises from simplicity. Truth is often emergent from repeated interactions rather than a single static fact.

SOUND: A drum beat that repeats, building a rhythm you can dance to.

SMELL: Baking bread: the yeast works its magic over and over.

TASTE: Layers of puff pastry made by folding dough again and again.

TOUCH: Feeling the ridges on corduroy fabric.

SIGHT: Watching a pendulum swing back and forth.

BODY: Walking: the repeated cycle of one foot in front of the other.

Music: All Too Well (10 Minute Version) (Taylor's Version) (From The Vault) by Taylor Swift

Music: You Were Meant to Be (feat. Glen Phillips) by Renee & Friends

Music: Porcelain by Moby

Part of Fractals & Self-Similarity — MATHEMATICS — Education Revelation