Golden Ratio Numbers

#!/usr/bin/env python3
# golden_ratio_patterns.py - Interactive φ Run Finder with curses UI
# pip3 install mpmath --break-system-packages
# python3 golden_ratio_patterns.py
import curses
import sys
import time
from mpmath import mp

DIGITS = 333_333_333  # Calculate 333 million digits to find all 9 patterns

# digit '0'..'9' → curses color_pair index (for runs ≥ 2)
RUN_COLOR_MAP = {
    '0': 2,  '1': 2,  '2': 3,  '3': 3,  '4': 4,
    '5': 4,  '6': 5,  '7': 5,  '8': 6,  '9': 6,
}

# run-length n → highlight color_pair index
HIGHLIGHT_PAIR = {2:2, 3:4, 4:3, 5:7, 6:8, 7:9, 8:10, 9:11}

# Known patterns in φ
KNOWN_PATTERNS = {
    2: ("33", 7),
    3: ("222", 131),
    4: ("4444", 1218),
    5: ("99999", 6401),
    6: ("555555", 99790),
    7: ("5555555", 771952),
    8: ("55555555", 771952),
    9: ("333333333", 314529196),
}

def print_legend(header_win, width):
    header_win.addstr(1, 2, "Len: ", curses.A_BOLD)
    col = 7
    for n in range(2, 10):
        digit = KNOWN_PATTERNS[n][0][0]
        label = f"{n}={digit}"
        attr = curses.A_REVERSE | curses.color_pair(HIGHLIGHT_PAIR[n])
        if col + len(label) + 2 < width - 2:
            header_win.addstr(1, col, label, attr)
            col += len(label) + 1

def curses_main(stdscr):
    curses.curs_set(0)
    curses.start_color()
    curses.use_default_colors()

    for i, c in enumerate([curses.COLOR_WHITE, curses.COLOR_RED, curses.COLOR_GREEN,
        curses.COLOR_YELLOW, curses.COLOR_BLUE, curses.COLOR_MAGENTA, curses.COLOR_CYAN,
        curses.COLOR_BLUE, curses.COLOR_MAGENTA, curses.COLOR_RED, curses.COLOR_YELLOW], 1):
        curses.init_pair(i, c, -1)

    h, w = stdscr.getmaxyx()
    if h < 20 or w < 80:
        stdscr.addstr(0, 0, "Terminal too small. Resize to at least 80×20.")
        stdscr.getch()
        return

    header_win = curses.newwin(10, w, 0, 0)
    digit_win = curses.newwin(h - 10, w, 10, 0)
    digit_win.scrollok(True)
    digit_win.idlok(True)

    title = "★ φ-Run Finder (333M digits, lengths 2…9) ★"
    header_win.addstr(0, max(0, (w // 2) - (len(title) // 2)), title, curses.A_BOLD)
    print_legend(header_win, w)
    for n in range(2, 10):
        header_win.addstr(n, 2, f"Len {n}: searching...")
    header_win.refresh()

    digit_win.addstr("Computing φ to 333,333,333 digits...\n", curses.color_pair(4))
    digit_win.refresh()

    compute_start = time.time()
    mp.dps = DIGITS + 100
    phi_str = mp.nstr((1 + mp.sqrt(5)) / 2, DIGITS + 2, strip_zeros=False)
    compute_time = time.time() - compute_start

    digit_win.addstr(f"Computed {len(phi_str)-2:,} digits in {compute_time:.1f}s\n\n", curses.color_pair(3))
    digit_win.refresh()
    time.sleep(1)

    total_pos, run_char, run_len = 0, None, 0
    remaining, start_time = set(range(2, 10)), time.time()

    for ch in phi_str:
        total_pos += 1
        if not ch.isdigit():
            run_char, run_len = None, 0
            continue

        run_len = run_len + 1 if ch == run_char else 1
        run_char = ch

        if run_len in remaining:
            n, start_pos = run_len, total_pos - run_len + 1
            elapsed, seq = time.time() - start_time, run_char * n
            if elapsed >= 3600:
                time_str = f"{int(elapsed//3600)}h {int((elapsed%3600)//60)}m"
            elif elapsed >= 60:
                time_str = f"{int(elapsed//60)}m {elapsed%60:.1f}s"
            else:
                time_str = f"{elapsed:.3f}s"

            info = f"Len {n}: {seq} @ {start_pos:,}   [{time_str}]"
            hl_attr = curses.A_REVERSE | curses.color_pair(HIGHLIGHT_PAIR[n])
            header_win.move(n, 2)
            header_win.clrtoeol()
            header_win.addstr(n, 2, info[:w-4], hl_attr)
            header_win.refresh()
            curses.beep()
            time.sleep(1)
            remaining.remove(n)

        pair = curses.color_pair(RUN_COLOR_MAP.get(run_char, 1)) if run_len >= 2 else curses.color_pair(1)
        if run_len >= 2 and run_char in '13579': pair |= curses.A_BOLD
        try:
            digit_win.addstr(ch, pair)
        except curses.error:
            pass
        digit_win.refresh()

    total_time = time.time() - start_time
    time_str = f"{int(total_time//3600)}h {int((total_time%3600)//60)}m" if total_time >= 3600 else f"{int(total_time//60)}m"
    digit_win.addstr(f"\n\n═══ COMPLETE ═══ All 9 patterns found in {time_str}\n", curses.color_pair(3) | curses.A_BOLD)
    digit_win.addstr("Press any key to exit.")
    digit_win.refresh()
    stdscr.nodelay(False)
    stdscr.getch()

def main():
    print("★ φ-Run Finder ★")
    print(f"Target: {DIGITS:,} digits")
    print("Starting curses interface...\n")
    curses.wrapper(curses_main)

if __name__ == "__main__":
    main()