TupperTransformer

An interactive demo of my Tupper's function transformation algorithm (pre-print from 2018), -Prathamesh Deshmukh.

$$ \frac{1}{2} < \left\lfloor \operatorname{mod}\left(\left\lfloor \frac{y}{17} \right\rfloor 2^{-17\lfloor x \rfloor - \operatorname{mod}(\lfloor y \rfloor, 17)}, 2\right) \right\rfloor $$

| Quick summary of the paper

k+17

You can also draw directly on the plot to create your own patterns.

Transform Pattern

Hold buttons to move the pattern on the canvas.

Current K-Value:

Load a pre-defined pattern or watch a demo.

Animation Demo (Eg3.1)

Plays the "Top-Left UFO" animation from the paper.

Interactive Tetris (Eg3.2)

After loading, the transform controls below the canvas will change to Tetris-specific controls.

Library of Babel

Continuously generates random K-values.

References

About TupperTransformer

Abstract

"My research idea start with a question that if there is some graphical formation at a particular value of k then what can do to change the graphical formation or to change its position. In his research paper, I have shown that:

How to change any graphical formation into other graphical formation by applying some kind of operation to the value of the k
How can this different graphical formation be used as a frame to create a film/motion picture

The Core Algorithm (My Original Research)

The technical paper that this project implements is my 2018 preprint, which provides the complete mathematical foundation for these operations.

Paper: "Transformation of the pixels in Tupper's self-referential formula"
Author: Prathamesh Deshmukh (Me)
Publication Date: May 24, 2018

The core idea I explored in the paper is that any graphical formation plotted by Tupper's formula (in the $106 \times 17$ grid) can be transformed by applying arithmetic operations directly to the `k` constant.

This algorithm allows for precise transformations, including:

Pixel Manipulation: Adding or removing any individual pixel `i` by adding or subtracting the value $17 \times 2^{i-1}$ from the `k` constant. (Equation C)
Spatial Translation (Moving):
- Up/Down: Moving the entire image `n` pixels up or down by multiplying or dividing `k` by $2^n$.
- Left/Right: Moving the entire image `n` pixels left or right by multiplying or dividing `k` by $2^{n \times 17}$.

How to Use This Demo

Select a mode: Transform & Load, Draw, or Demos & Examples.
The demo will load the relevant example from my paper or a blank canvas.
Use the contextual controls for each mode to transform the image.
See the resulting `k` value and the updated image in real-time.

Citation & Publication History

BibTeX Citation (Recommended)

@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"
}

Indexing & Archives

Preferred Version (Figshare v2)

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

First Posted: June 08, 2018

https://doi.org/10.6084/m9.figshare.6373046 → Access the full article here

Semantic Scholar Index

https://www.semanticscholar.org/paper/Transformation-of-the-Pixels-in-Tupper's-Formula-Deshmukh/f7f02b429a5fcdc20a29410226c73eecaf992541

Internet Archive (Archive of v1)

httpsE://web.archive.org/web/20200220095114/https://s3-eu-west-1.amazonaws.com/pfigshare-u-files/11711468/Transformation_of_pixels.pdf