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Hi Hamid, I am Yusuf. I came across your mountains post from yesterday 25/4, and it stopped me completely. I decided to push myself to the limit and implement your formula from scratch, pixel by pixel, as a personal mathematical challenge. After careful study of the image, I have successfully identified and understood 12 of the 14 mathematical objects: ✓ F(x) — color compression to [0, 255] ✓ N_s(x,y) — fractal noise with 6^5 * 5^(-s) frequency scaling ✓ E(x,y) — fractal envelope as a 50-term weighted sum ✓ Z_s(x,y) — layer occlusion product ✓ S(x,y) — sky value ✓ R(x,y) — layer depth value ✓ T(x,y) — distance to mountain center ✓ B(x,y) — slope angle via arctan ✓ A(x,y) — layer brightness ✓ H_v(x,y) — final color channel for v = 0, 1, 2 ✓ Coordinate mapping: x = (m-1000)/600, y = (601-n)/600 ✓ The full N_s structure The two I cannot read precisely enough from the image are: ✗ J_s(x,y) — the mountain shape indicator ✗ K_v(x,y) — the lighting kernel I can see the general structure of both. J_s uses a double exponential with cosine products and E(x,y)/1000 in the exponent, and K_v sums 50 terms of (91/100)^s weighted by cosines involving T, B and v. But the exact coefficients inside the ridge shape term of J_s and the cosine arguments of K_v are too dense to read at the resolution I have. What I am currently seeing in my attempts: the layering and occlusion work correctly and the fractal texture E renders as expected, but without the exact J_s the mountain silhouettes are wrong. Peaks appear at incorrect positions and the snow and rock boundary does not match your image. This is purely a personal challenge. I am not doing this for any commercial purpose. Could you point me to where the full formula is published, or share a higher resolution crop of the equation panel from that post? Even just confirming those two functions would be enough to complete the implementation. Thank you. Yusuf

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My wife collapsed in our hotel room in New York today “Call an ambulance, I can’t breathe” she was screaming My heart dropped If she ends up in an American hospital we are financially ruined I went on the Lufthansa app to book a flight back to Frankfurt, but unfortunately pilots are on strike today “Please I’m begging you” she was lying on the floor I sighed and called 911 She is now in surgery as apparently her appendix “almost burst” I am extremely scared This is going to cost us at least $100,000 She could have received much better care, for free, in Germany I will never visit this barbaric country ever again