CollatzConjecture

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  collatz conjecture with the number 27

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  collatz conjecture with the number 300

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  collatz conjecture from 1 to 30

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  collatz conjecture using a small difference in angle change per step

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  collatz conjecture eminating from a sphere's circumference

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  collatz conjecture from 1 to 100

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  collatz conjecture from 1 to 100 randomly distributed from sphere

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  collatz conjecture from 150 to 300 distributed from sphere using a helix function

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  collatz conjecture from 1 to 300 randomly distributed from sphere

Problem We wondered How can we produce similarly beautiful art generated with our own creative approach to any arbitrary function, similar to the collatz conjecture

Solution Any function can be tuned to output an array of boolean values So, by writing generalized visualization functions to boolean array inputs, we can produce visuals for any function that can be tuned to output an array of booleans There are two components to any visualization The mathematical function adjusted to output a boolean array The visualization method used to interpret the boolean array into 3D coordinates, which are then graphed using splines Technologies used Java Processing P3D Challenges Getting colors, particularly gradients of colors Merging code Large input sizes Growth/Things Using interfaces to generalize more Each function was already tuned to have identically named functions for producing the array of booleans, and each illustrative method also shared function names, but we never got around to combining everything Optimality The code is pretty slow, making the already laggy visualization software even slower Accomplishments They look cool We have never worked with 3D until now, and we had success working on separate sides of the project and having them combine as planned to produce images

Built With

• java
• p3d
• processing