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J/SH M/LLARD /INTERACT/ON DES/GN STUDENT.

(SEE MY WORK ON DESKTOP:)


—Processing —chaos theory

“LORENZ _ATTRACTOR”

HUBRET.GQ /// Partner

"Processing for Mathematical Sublime"


A visual representation of working Chaos Theory, concerning deterministic systems whose behavior can in principle be predicted, when in actuality, they are far too sensitive to predict accurately over time.

This is a 2D Processing rendition of that system, making use of the Lorenz Equations that are used to predict weather, robotic balance, and inspire the butterfly effect through Bifurcation.

Divergence

This sequence is not a singular unit, but rather a visual representation of the difference area between two systems with slightly different starting conditions.

/// Finding-Sublime

It seems to be this shifting of balance between chaos and order, that viewers resonate with, and what makes the movement seem so life like and sentient despite its mathematical origins.

*   The pattern can be felt and perceived but its exact nature is always just out of reach.


Mathematical Model

dx/dt = o(y-z)
dy/dt = x(p-z)-y
dz/dt = xy - bz

Chaotic Systems

x,y,z  = dimensions
t   = time
o,p,b  = system parameters

/// Initial Process

Verified by the updating readout on the right side of the sketch, the code produced chaotic solutions based on the Lorenz Attractor functions.

A line is plotted at the x,y coordinates produced by the math every frame. It shows in 2D, the simple build up that typical attractors showcase in 3D.


HUD

The two boxes on the left show the random initial conditions of each attractor to prove that the systems are only slightly dissimilar.

The numbers on the right are real time solutions to each equation which is also the coordinate location for rendering its point on the sketch.

/// Final-Sketch

In order to exemplify the nature of chaos theory of wildly diverging outcomes, two Lorenz Attractors are drawn from similar initial starting conditons. When they are close they change color and when they are not they layer their shape onto the canvas in an after-image.

Full_process_doc.pdf