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#!/usr/bin/env python3
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"""
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interference.py - wave interference patterns
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​
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Two sources, rippling outward, overlapping.
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What happens when waves meet?
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​
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Just physics. Just patterns.
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"""
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​
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import math
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​
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def interference_pattern(width=60, height=30, time=0, source1=(15, 15), source2=(45, 15)):
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    """Generate an interference pattern from two wave sources."""
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​
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    # Characters for different intensities
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    chars = " .·:+*#@"
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​
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    pattern = []
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​
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    for y in range(height):
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        row = []
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        for x in range(width):
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            # Distance from each source
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            d1 = math.sqrt((x - source1[0])**2 + (y - source1[1])**2)
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            d2 = math.sqrt((x - source2[0])**2 + (y - source2[1])**2)
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​
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            # Wave from each source (with time evolution)
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            wavelength = 4.0
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            wave1 = math.sin(2 * math.pi * d1 / wavelength - time)
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            wave2 = math.sin(2 * math.pi * d2 / wavelength - time)
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​
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            # Interference: waves add
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            combined = (wave1 + wave2) / 2
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​
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            # Map to character
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            intensity = int((combined + 1) / 2 * (len(chars) - 1))
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            intensity = max(0, min(len(chars) - 1, intensity))
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            row.append(chars[intensity])
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​
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        pattern.append(''.join(row))
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​
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    return '\n'.join(pattern)
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​
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​
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def animate(frames=12):
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    """Show how the pattern evolves over time."""
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    print("Wave Interference Pattern")
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    print("Two sources, meeting in space")
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    print("=" * 60)
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    print()
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​
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    for t in range(frames):
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        time = t * 0.5
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        print(f"[t = {time:.1f}]")
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        print(interference_pattern(time=time))
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        print()
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​
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​
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def still():
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    """Just one moment. Frozen."""
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    print("Wave Interference - Still")
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    print("=" * 60)
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    print()
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    print(interference_pattern(time=0))
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    print()
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    print("Where the waves align: constructive interference (bright)")
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    print("Where they cancel: destructive interference (dark)")
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    print("The pattern isn't in either wave. It's in the meeting.")
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​
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​
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if __name__ == "__main__":
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    # Show a few frames
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    animate(frames=6)
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​
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    print("\n" + "=" * 60)
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    print("Moving the sources closer together...")
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    print("=" * 60 + "\n")
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​
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    # What happens when sources are closer?
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    print(interference_pattern(time=0, source1=(25, 15), source2=(35, 15)))
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    print()
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    print("Closer sources = wider spacing between the bright lines")
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    print("(That's real physics. That's how diffraction gratings work.)")
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​