Prime spiral generator

Inspired by 3b1b's video on prime spirals and more.
Generates unique prime spirals with Python and matplotlib.
The script plots prime numbers with a random colour map onto a grid using polar coordinates.
It used to use Sieve of Eratosthenes which is like O(N log (log N)) but now it uses a caching system you can check that out in gen_scripts/prime_gen and choose which one to use in gen_scripts/ps_plt_gen.py.
Actually the sieve is faster im not sure why im gonna optimise the cache method.

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Sample images

Sample outputs (from sample_images/):

Random spiral #2	Random spiral #9	Random spiral #12

Random spiral #15	Random spiral #17	Random spiral #19

sample_images/ includes 20 sample images

Sample grid outputs (from grid_images/):

4 by 4 grid

33 by 33 grid

sample_images/ includes 2 sample grids

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Installation

Requirements

• Python 3.10+

  matplotlib
  random
  math
  

Setup

1. Clone this repository:

   git clone https://github.com/ethanwang314159/prime-spiral-generator.git
   cd prime-spiral-generator

2. Install dependencies:

   pip install -r requirements.txt

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Usage

python main.py

Generates 16 unique spirals and then a 4 by 4 grid with those spirals into rand_images and grid_images.

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File Structure

prime-spiral-generator/
│
├── gen_scripts/
│   ├── next_fp_gen.py          # Finds next available file path in folder
│   ├── ps_plt_gen.py           # Generates prime spiral plot (returns plt)
│   ├── rand_settings_gen.py    # Creates random settings
│   ├── grid_gen.py             # Generates a grid of spirals
│   ├── empty_folder_gen.py     # 
│   └── prime_gen
│       ├── get_primes_cache.py # Getting primes with cache
│       ├── get_primes_sieve.py # Getting primes with sieve
│       ├── primes_cacher.py    # Cacheing primes 
│       ├── primes_cache.rs     # Cached primes storage
│
├── rand_images/                # Empty (for now)
│
├── temp_images/                # Temp images for large grid generation(not saving each spiral)
│
├── sample_images/
│   └── 0.png ... 19.png        # Sample images
│
├── grid_images/
│   └── grid0.png               # 4x4 Sample grid image
│   └── grid1.png               # 33x33 Sample grid image
│
└── main.py                     # Main script for spiral generation

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Todo

• Animation: visualise the spirals forming like the primes getting loaded in (maybe gifs).
• Interactive: adjustable spiral settings in a good ui. like change the size by dragging/clicking not typing a number.
• Vote: a website where you vote between two spirals and using an algorithm like the elo system find the perfect spiral with a leaderboard etc
• Optimise: make it faster
• Tweak the settings: make it better