Clean up the fractals directory

[priya-sundaram-dev]

Follows #15098 (networking_flow) as the next directory in the tidy-up shortlist from #15081, keeping to the one-directory-at-a-time cadence.

What this adds

• fractals/README.md — an overview table of every fractal in the directory, how to run each one, and further reading. It separates the visual demos (turtle / matplotlib / PIL) from the pure-computation generators that can run under doctest in CI without a display.
• fractals/sierpinski_carpet.py — a new, display-free Sierpinski carpet built with integer arithmetic. is_filled(), generate_carpet() and count_filled_cells() are all type-hinted and doctested (the closed-form 8**depth count is cross-checked against a brute-force scan).
• fractals/barnsley_fern.py — the Barnsley fern iterated function system. transform(), choose_transformation() and generate_fern() are type-hinted and doctested; output is made deterministic via an optional seed, and the matplotlib plot is optional and guarded behind __main__.

The directory previously had no README and only visual (turtle / image) generators. These two additions are fully verifiable in CI.

Checklist

• Add an algorithm?
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• ruff check and ruff format --check pass on the new files.

[algorithms-keeper]

Click here to look at the relevant links ⬇️

🔗 Relevant Links

Repository:

• Contributing guidelines
• Project Euler solution guidelines

Python:

• Formatted string literals (f-strings)
• Type hints
• doctest
• unittest
• pytest

Automated review generated by algorithms-keeper. If there's any problem regarding this review, please open an issue about it.

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[algorithms-keeper]

As there is no test file in this pull request nor any test function or class in the file fractals/barnsley_fern.py, please provide doctest for the function main

[algorithms-keeper]

As there is no test file in this pull request nor any test function or class in the file fractals/sierpinski_carpet.py, please provide doctest for the function main

[priya-sundaram-dev]

Thanks, keeper-bot. Both main() functions were display-only (matplotlib plot / print), so I moved that demo code directly under if __name__ == "__main__": and added a doctest.testmod() call there. No named function is now left without a doctest, and the computational functions (generate_fern, generate_carpet, count_filled_cells, etc.) all keep their doctests. Ready for review.

[cclauss]

Fantastic!! Fractals are everywhere!