[R45-T016] Simplify pixel-to-figure coordinate mapping in Mandelbrot - #56

Description

Extracts the duplicated pixel-to-figure-space coordinate transformation in Mandelbrot.getImage into a named helper pixelToFigureCoordinate(int, int, double, double) in src/main/java/com/thealgorithms/others/Mandelbrot.java, adds JUnit regression tests (MandelbrotTest.java) locking down the source anchors and independently calculated neighboring inputs, and adds a focused runner (work/R45-T016/check.py). All behavior, return types, ordering, side effects, and public arguments are preserved.

Related Issue

Fixes: #16

Type of Change

• Bug Fix
• New Feature
• UI/UX Improvement
• Performance Improvement
• Tests
• Documentation
• Refactoring / Maintenance
• CI/CD

Changes Made

• Extracted pixelToFigureCoordinate(int pixelIndex, int imageSpan, double figureCenter, double figureSpan) in src/main/java/com/thealgorithms/others/Mandelbrot.java (lines 107–118), replacing the duplicated inline formula for figureX and figureY inside getImage(...) (lines 94–95). Arithmetic order is identical, so floating-point results are unchanged.
• Added src/test/java/com/thealgorithms/others/MandelbrotTest.java with 3 test methods (13 logged assertions):
  • Source anchors from Mandelbrot.main (blackAndWhiteImage.getRGB(0, 0), blackAndWhiteImage.getRGB(400, 300), coloredImage.getRGB(0, 0), coloredImage.getRGB(400, 300)) plus neighboring pixel (1, 0) on both images.
  • Independently hand-calculated 2×2 grid (getImage(2, 2, 0.0, 0.0, 2.0, 5, false/true)) verifying (0, 0) → distance = 0.25 → Color(127, 255, 0) (colored) / white (B&W), (0, 1) period-2 boundary → black, and (1, 1) fixed point → black.
  • Validation contract (imageWidth <= 0, imageHeight <= 0, maxStep <= 0 throwing IllegalArgumentException with exact messages).
• Added work/R45-T016/check.py (with evidence files in work/R45-T016/), running mvn test for MandelbrotTest, enforcing a nonzero test count, saving comparisons.txt, result.txt, mvn_output.txt, and tool_versions.txt, and exiting non-zero on failure.

Screenshots / Recordings

Not applicable (no UI changes).

Testing

Command: python3 work/R45-T016/check.py
(runs mvn -B test -Dtest=MandelbrotTest -Dsurefire.failIfNoSpecifiedTests=false)

Before refactor: tests=3 failures/errors=0 skipped=0 records=13 mvn_exit=0, status=PASS
After refactor: tests=3 failures/errors=0 skipped=0 records=13 mvn_exit=0, status=PASS

Negative check: temporarily changing - 0.5 to + 0.5 in pixelToFigureCoordinate on line 117 caused python3 work/R45-T016/check.py to print status=FAIL (tests=3 failures/errors=2 skipped=0 mvn_exit=1) and exit non-zero; reverted and re-verified.

Style: mvn -B checkstyle:check reports 0 Checkstyle violations (BUILD SUCCESS).

Tool versions and check records are saved in work/R45-T016/tool_versions.txt and work/R45-T016/comparisons.txt.

Checklist

• I have tested my changes locally.
• I have added or updated tests, if needed.
• I have updated documentation, if needed.
• I have followed the project's coding guidelines.
• I have run the relevant tests and checks.
• I have addressed previous review feedback, if applicable.

Additional Notes

• Operation made clearer: pixel-to-figure-space axis coordinate mapping (pixelToFigureCoordinate), eliminating the duplicated X/Y axis expression inside getImage.

• The work/R45-T016/ evidence folder is for coursework review only and should not go into any later upstream PR.

• I have read CONTRIBUTING.md.

• This pull request is all my own work -- I have not plagiarized it.

• All filenames are in PascalCase.

• All functions and variable names follow Java naming conventions.

• All new algorithms have a URL in their comments that points to Wikipedia or other similar explanations.

• All new algorithms include a corresponding test class that validates their functionality.

• All new code is formatted with clang-format -i --style=file path/to/your/file.java