TupperTransformer

A Novel Image Processing Algorithm

Introduction

Note: This project is in a very early, experimental stage.

Welcome to the official page for the TupperTransformer project. This project is my exploration of a new image processing technique based on my 2018 preprint, "Transformation of the pixels in Tupper's self-referential formula."

The algorithm operates directly on the high-precision integer (k-value) used to generate Tupper's self-referential bitmaps, rather than manipulating the pixels after they are rendered. This page hosts the interactive demo that serves as the proof-of-concept and implementation of that research.

Live Demonstration

Check out the live, interactive demo to see this algorithm in action.

Launch Interactive Demo

About the Research

The research is based on Tupper's self-referential formula, famous for its ability to plot a visual representation of the formula itself. However, its capabilities extend far beyond self-reference; it can render every possible 106x17 bitmap image.

My research began with a fundamental question:

"If there is some graphical formation at a particular value of k, then what can be done to change the graphical formation or to change its position?"

This inquiry led to two main research thrusts:

Developing operations on the k-value to transform one graphical formation into another.
Using these transformations as frames to create animations or motion pictures.

Core Capabilities

Represent all possible graphical formations within the 1802-pixel grid.
Define a mathematical formula for any film or motion picture that can be rendered in this grid.

In essence, this research presents a mathematical framework for a "Library of Babel" for visual media.

Demo Instructions

The interactive demo is organized into a simple, tabbed interface.

1. Transform & Load (Main Panel)

This is the main editor. You can:

Load Examples: Load the classic "Tupper's" formula or a "UFO" image.
Transform: Use the directional buttons to modify the entire image.
Animate: Click and hold a transform button to create a temporary animation. Holding for 1 second latches the animation.

2. Draw

This panel demonstrates the reverse of the formula:

Click or drag on the canvas to toggle pixels.
The K-Value updates in real-time to reflect your drawing.

3. Demos & Examples

This tab showcases examples from the paper:

Animation Demo: See a UFO animated using the transformation formula.
Interactive Tetris: Move a single Tetris piece while others remain static.

Citation

If you use this work in your research, please cite the original preprint.

APA Style

Deshmukh, P. (2018). Transformation of the pixels in Tupper's self-referential formula. Figshare. https://doi.org/10.6084/m9.figshare.6373046

BibTeX

@article{Deshmukh2018,
  author  = "P Deshmukh",
  title   = "{Transformation of the pixels in tupper's self-referential formula}",
  year    = "2018",
  month   = "6",
  url     = "https://figshare.com/articles/preprint/Transformation_of_pixels_pdf/6373046",
  doi     = "10.6084/m9.figshare.6373046.v2"
}