PrimeImage

Find prime numbers in the shape of binary images

It does what now?

PrimeImage produces prime numbers to appear like arbitary (binary) images - for example this smiley face!

11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111881111111111188811111111111111111
11111111111111181118811111111811181111111111111111
11111111111111181111811111118111118111111111111111
11111111111111181111811111111811118111111111111111
11111111111111118888111111111888881111111111111111
11111111111111111111111111111111111111111111111111
11111111188111111111111111111111111111181111111111
11111111818111111111111111111111111111818111111111
11111111811811111111111111111111111118118111111111
11111111181881111111111111111111111118118111111111
11111111188188111111111111111111111881181111111111
11111111118811881111111111111111118111811111111111
11111111111181118881111111111118811188111111111111
11111111111118881111888888888811118811111111111111
11111111111111118888111111111188811111111111111111
11111111111111111111188888881111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111112251

In its current state the last few digits are mutated until a prime is found. The digits at the end are currently incremented by two (maintaining the odd property of the number), and a primality test is run on each number.

Usage

PrimeImage was written as a Python 3 project, for Python 2 I have not tested and cannot guarantee it'll work, due to the use of iterators.

To immediately jump in and have fun, run from terminal python3 primeimage -u, which will load a test image (my College's crest) and generate a prime that looks like it.

To load an arbitary image (at the moment the image should be square!), run python3 -i ~/path/to/image. Most common formats (.png, .jpg, .bmp etc) are supported.

Help can be loaded by using the -h flag.

Limitations (and todos!)

1. Histogram Equalisation is REQUIRED to make the distribution of numbers fair.
2. Subtle number abberation to force primality is required.
3. A 'force Binary' option may be useful.
4. For the moment the images are small, on the order of 25 x 50 pixels.
   • if you insist on a larger image you can change the size_x and size_y on the function call on line 192.
5. The y dimension has a lower spatial resolution (half of x dimension) due to the use of monospaced integers.
6. Prime number images are only binary (for now).
7. Images should be square. In an upcoming version adaptive sizing will be avaliable.
   • for now - if you really do insist on an arbitary dimensioned image you can change the size_x and size_y on the function call on line 192. Just be wary that size_y should be half what you expect, owing to monospaced numbers being twice high as wide.

Installation

PrimeImage needs a version of Python 3 installed (ver > 3.5).

PrimeImage needs the following packages:

1. scipy
2. numpy
3. matplotlib (in future generations)
4. time

Theory

A blog post was written on the theory, here