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priya-sundaram-dev
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* Clean up the fractals directory Add a directory README plus two new, fully doctested fractal generators. - README.md: overview table of every fractal, how to run them, and further reading. Distinguishes the visual (turtle/matplotlib) demos from the pure-computation ones that run under doctest in CI. - sierpinski_carpet.py: integer-arithmetic Sierpinski carpet. is_filled(), generate_carpet() and count_filled_cells() are all doctested; no display needed. - barnsley_fern.py: the Barnsley fern iterated function system. transform(), choose_transformation() and generate_fern() are doctested and made deterministic via an optional seed; matplotlib plotting is optional and guarded behind __main__. * fractals: inline demo code under __main__ (address keeper-bot doctest note)
45 lines
1.9 KiB
Markdown
45 lines
1.9 KiB
Markdown
# Fractals
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A fractal is a geometric figure that is *self-similar*: zooming into a piece of
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it reveals a copy of the whole. Fractals show up in mathematics, physics,
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computer graphics and even biology (coastlines, ferns, snowflakes).
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This directory collects small, self-contained fractal generators. They fall
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into two groups:
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- **Visual demos** that open a window (via `turtle`) or produce an image
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(via `matplotlib`/`PIL`). Run these directly to see the picture.
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- **Pure-computation** generators whose output can be checked with `doctest`,
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so they run in CI without a display.
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## Contents
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| File | Fractal | Output | Notes |
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| ---- | ------- | ------ | ----- |
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| [`barnsley_fern.py`](barnsley_fern.py) | Barnsley fern | matplotlib (optional) | Iterated function system; deterministic with a seed |
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| [`julia_sets.py`](julia_sets.py) | Julia sets | matplotlib | Complex-plane escape-time fractal |
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| [`koch_snowflake.py`](koch_snowflake.py) | Koch snowflake | matplotlib | Line-segment subdivision |
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| [`mandelbrot.py`](mandelbrot.py) | Mandelbrot set | PIL image | Complex-plane escape-time fractal |
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| [`sierpinski_carpet.py`](sierpinski_carpet.py) | Sierpinski carpet | text | Integer arithmetic, fully doctested |
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| [`sierpinski_triangle.py`](sierpinski_triangle.py) | Sierpinski triangle | turtle | Recursive midpoint subdivision |
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| [`vicsek.py`](vicsek.py) | Vicsek fractal | turtle | Recursive cross pattern |
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## Running
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```bash
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# text fractal – prints to the terminal
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python fractals/sierpinski_carpet.py
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# image fractal – opens a matplotlib window (needs matplotlib)
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python fractals/barnsley_fern.py
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# turtle fractal – opens a drawing window (needs a display)
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python fractals/vicsek.py
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```
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## Further reading
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- Benoit B. Mandelbrot, *The Fractal Geometry of Nature* (1982)
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- Michael Barnsley, *Fractals Everywhere* (1988)
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- <https://en.wikipedia.org/wiki/Fractal>
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