lamp: square ξ image so the quarter turn still fills the frame; sharper brightness

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01FAqjv3n4yABxvJPJHFRhVA

src/lamp/xi_image.py

@@ -1,9 +1,9 @@
-# Paint xi in the u-chart, u = 1/(4(s - 1/2)), as a 1920x1080 PNG (supersampled 2x), and trace the |xi| = 1 contour (the edge of the dark cone).
+# Paint xi in the u-chart, u = 1/(4(s - 1/2)), as a square 1920x1920 PNG (supersampled 2x; the frame shows the middle 16:9 of it, so a quarter turn still fills the frame), and trace the |xi| = 1 contour (the edge of the dark cone).
 import numpy as np, json
 from scipy.special import loggamma
 from PIL import Image
-W, H, SS = 1920, 1080, 2
-HW_Y = 0.016                     # half-height of the window in u
+W, H, SS = 1920, 1920, 2
+HW_Y = 0.02844                    # half-height of the window in u
 PPU = H*SS/(2*HW_Y)              # pixels per unit of u (supersampled)
 BC = [1/12,-1/720,1/30240,-1/1209600,1/47900160,-691/1307674368000,1/74724249600,-3617/10670622842880000,43867/5109094217170944000,-174611/802857662698291200000]
 N = 160
@@ -29,7 +29,7 @@ ok = r2 > (1/(4*900))**2                              # |s - 1/2| < 900: within
 L[ok] = log_xi(s[ok])
 mag, ph = L.real, L.imag
 h = (ph/(2*np.pi)) % 1.0
-v = 0.14 + 0.74*(0.5 + np.arctan(0.7*mag/2.5)/np.pi)
+v = 0.14 + 0.74*(0.5 + np.arctan(0.7*mag/1.5)/np.pi)
 v = np.where(ok, v, 0.16); h = np.where(ok, h, 0.0); sat = np.where(ok, 0.62, 0.0)
 # hsv -> rgb
 i = np.floor(h*6).astype(int) % 6; f = h*6 - np.floor(h*6)