Each verse becomes a rippled ring. Its letter count sets the radius, its word count sets the number of ripples, and variation in word length sets their depth. The rings rise and rotate in verse order.
R = 40 + 2L A = 0.25σᵥ / (μᵥ + σᵥ) r(θ) = R[1 + A cos(Wθ)]
W and L are the verse’s word and letter counts; μᵥ and σᵥ are its mean word length and population standard deviation. For verse i of V, rotation is 2π(i − 1)/V and height is 12(i − 1). The tilted view projects y to 0.42y − 0.907[z − 6(V − 1)].
Read every word as a movement. A word of length ℓ draws an arc of length 10ℓ. Longer-than-average words turn left; shorter words turn right. Each arc continues from the previous one, so word order changes the drawing.
μ and σ describe all word lengths in the surah. The path begins at (0, 0), facing right; each circular arc changes its heading by Δ, capped smoothly at ±135°. Zero turn draws a straight line. If σ = 0, the whole path is straight.
Each ayah becomes one horizontal line. Its letter count sets its length. The lines are centered and stacked in verse order, revealing the rhythm of short and long passages.
Length = 6L xₗ = −3L; xᵣ = 3L y = 12(i − 1)
L is the ayah’s retained letter count and i is its verse number. Subtle divisions mark word boundaries where space allows. A single scale fits the whole drawing, so a verse with twice as many letters produces a line twice as long.
