use a stair step sigmoid to repeat gradient steps of cilia density

src/shimmers/math/equations.cljc

@@ -186,3 +186,17 @@
 ;; https://stackoverflow.com/a/34576808/34450
 (defn flat-smooth [x]
   (+ x (- x (* (sqr x) (- 3.0 (* 2.0 x))))))
+
+;; https://math.stackexchange.com/a/2529617/903738
+(defn stair-sigmoid
+  [height hscale hoffset alpha x]
+  (let [m (- (/ 1 (+ 1 (math/exp (- alpha)))) 0.5)
+        term (- (* hscale x) hoffset 0.5)
+        r (- term (math/floor term) 0.5)]
+    (* height (+ (math/floor term)
+                 (* (/ 1.0 (* 2.0 m))
+                    (- (/ 1.0 (+ 1.0 (math/exp (* -2.0 alpha r)))) 0.5))
+                 1))))
+
+(comment (map (fn [x] (stair-sigmoid 0.1 10.0 0 1 x))
+              (range 0 1 (/ 1.0 30))))

src/shimmers/sketches/cilia_phase.cljs

@@ -92,7 +92,8 @@
                            :random 0.5
                            :random-normal 0.66
                            :stripes 1.5
-                           :sin-stripes 1.0})
+                           :sin-stripes 1.0
+                           :stair-sigmoid 1.33})
         proportion
         (dr/weighted {6 1.0
                       5.0 1.0
@@ -117,6 +118,9 @@
           :div-prime div-prime})
        :sin-stripes
        {:freq (dr/random 0.66 1.33)}
+       :stair-sigmoid
+       {:freq (dr/random-int 2 32)
+        :alpha (dr/random 1.0 3.0)}
        {}))))
 
 (defn samples-from-density [{:keys [mode density] :as pts}]
@@ -142,7 +146,12 @@
         (/ (mod (* x mul-prime) div-prime) div-prime)))
     :sin-stripes
     (for [x (range -0.05 1.05 (/ 1.0 density))]
-      (eq/unit-sin (* eq/TAU (:freq pts) x)))))
+      (eq/unit-sin (* eq/TAU (:freq pts) x)))
+    :stair-sigmoid
+    (let [freq (:freq pts)
+          alpha (:alpha pts)]
+      (for [x (range -0.05 1.05 (/ 1.0 density))]
+        (eq/stair-sigmoid (/ 1.0 freq) freq 0 alpha x)))))
 
 (defn line-parameters []
   (let [n (dr/weighted {(dr/random-int 3 8) 3.0