Phase vectors, update examples

CHANGELOG.md

@@ -2,6 +2,26 @@
 
 ## [unreleased]
 
+- #70:
+
+  - Adds
+
+    - `emmy.mathbox.physics.{phase-vectors,lagrangian-phase-vectors,hamiltonian-phase-vectors,routhian-phase-vectors}`
+      for building out phase portraits like those in the Phase Portrait and
+      Quartic Well examples.
+
+    - many geodesics to the Klein bottle examples.
+
+    - a matrix basis visualization example to `examples.mathbox.geom`.
+
+  - `ode-curve` now sets `:simplify?` to `false` by default.
+
+  - Converts the phase portrait and quartic well examples to use all server side
+    code and components.
+
+  - `emmy.viewer.components.physics/Evolve` now adds a `:tick` entry into its
+    state to force re-renders, since the `:state` array is mutable.
+
 - #69:
 
   - Adds

dev/emmy_viewers/mathbox.clj

@@ -12,8 +12,6 @@
 
 ;; ## Server-Side MathBox
 
-(def ->tex (comp clerk/tex ->TeX simplify))
-
 {::clerk/width :wide}
 
 ^{::clerk/visibility {:code :hide :result :hide}}

dev/emmy_viewers/notebook.clj

@@ -316,6 +316,7 @@
 ;; - [examples.manifold.pq-knot](/dev/examples/manifold/pq_knot)
 ;; - [examples.mathbox.cube-controls](/dev/examples/mathbox/cube_controls)
 ;; - [examples.mathbox.functions](/dev/examples/mathbox/functions)
+;; - [examples.mathbox.feig](/dev/examples/mathbox/feig)
 ;; - [examples.mathbox.geom](/dev/examples/mathbox/geom)
 ;; - [examples.mathbox.ode](/dev/examples/mathbox/ode)
 ;; - [examples.mathbox.quickstart](/dev/examples/mathbox/quickstart)

dev/emmy_viewers/sci_extensions.cljs

@@ -4,8 +4,6 @@
   (:require [emmy.viewer.sci]
             [examples.simulation.cylinder-flow]
             [examples.simulation.lorenz]
-            [examples.simulation.phase-portrait]
-            [examples.simulation.quartic-well]
             [nextjournal.clerk.sci-env]))
 
 (emmy.viewer.sci/install!)

dev/examples/expression.clj

@@ -2,10 +2,11 @@
 (ns examples.expression
   {:nextjournal.clerk/toc true}
   (:refer-clojure
-   :exclude [+ - * / = zero? compare numerator denominator ref partial])
+   :exclude [+ - * / = zero? compare abs
+             numerator denominator ref partial infinite?])
   (:require [nextjournal.clerk :as clerk]
             [nextjournal.clerk.viewer :as-alias viewer]
-            [emmy.env :as e :refer [+ * / ->TeX cos expt sin square]]
+            [emmy.env :as e :refer :all]
             [emmy.clerk :as ec]
             [reagent.core :as-alias reagent]))
 
@@ -25,17 +26,16 @@
 ;; We can convert this to LaTeX, but clerk won't know what to do with the
 ;; string.
 
-(->TeX
+(ec/->TeX
  (+ (square (sin 'x))
     (square (cos 'x))))
 
-;; We can do better by invoking `clerk/tex` to tell Clerk to interpret this
-;; string as TeX:
+;; We can do better by invoking `emmy.clerk/->TeX` to tell Clerk to interpret
+;; this string as TeX:
 
-(clerk/tex
- (->TeX
-  (+ (square (sin 'x))
-     (square (cos 'x)))))
+(ec/->TeX
+ (+ (square (sin 'x))
+    (square (cos 'x))))
 
 ;; Try it out:
 

dev/examples/mafs.clj

@@ -131,12 +131,9 @@
 ;;
 ;; tabbed viewer between TeX and plot:
 
-(def ->tex
-  (comp clerk/tex ->TeX simplify))
-
 (let [f ((expt D 5) tanh)]
   (ec/multi
-   {:TeX  (->tex (f 'x))
+   {:TeX  (ec/->TeX (f 'x) :simplify? true)
     :Mafs (mafs/mafs
            {:zoom {:min 0.1 :max 2}}
            (mafs/cartesian)
@@ -264,7 +261,7 @@
 
 (let [f ((expt D 3) tanh)]
   (clerk/col
    (->tex (f 'x))
    (mafs/mafs {:zoom {:min 0.1 :max 2}}
               (mafs/cartesian)
               (mafs/of-x f {:color :blue}))))

dev/examples/mafs/edit.clj

@@ -3,7 +3,6 @@
    :nextjournal.clerk/doc-css-class [:overflow-hidden :p-0]}
   (:require [nextjournal.clerk :as clerk]))
 
-
 (clerk/with-viewer
   {:render-fn 'nextjournal.clerk.render.editor/view
    :transform-fn clerk/mark-presented}

dev/examples/mathbox/color_test.clj

@@ -0,0 +1,35 @@
+^{:nextjournal.clerk/visibility {:code :hide}}
+(ns examples.mathbox.color-test
+  #:nextjournal.clerk{:toc true}
+  (:refer-clojure
+   :exclude [+ - * / = zero? compare numerator denominator ref partial
+             infinite? abs])
+  (:require [emmy.clerk :as ec]
+            [emmy.leva]
+            [emmy.env :as e :refer :all]
+            [emmy.mathbox.plot :as plot]
+            [emmy.viewer :as ev]))
+
+{:nextjournal.clerk/width :wide}
+
+^{:nextjournal.clerk/visibility {:code :hide :result :hide}}
+(ec/install!)
+
+;; # Color Testing
+
+;; ## Demo
+;;
+;; Let's make a function to try!
+
+(ev/with-let [!state {:amplitude 1}]
+  (plot/scene
+   (emmy.leva/controls {:atom !state})
+   (plot/of-xy
+    {:x-samples 128
+     :y-samples 128
+     #_#_:color "LimeGreen"
+     :z (ev/with-params {:atom !state :params [:amplitude]}
+          (fn [amplitude]
+            (fn [[x y]]
+              (* amplitude
+                 (cos (* x y))))))})))

dev/examples/mathbox/feig.clj

@@ -0,0 +1,71 @@
+;; # Feigenbaum
+
+(ns examples.mathbox.feig
+  {:nextjournal.clerk/toc true}
+  (:require [emmy.clerk :as ec]
+            [emmy.mathbox :as mb]
+            [nextjournal.clerk :as clerk]))
+
+^{::clerk/visibility {:code :hide :result :hide}}
+(ec/install!)
+
+(defn f [p x] (* p x (- 1 x)))
+
+(defn fixps [r]
+  (->> (iterate (partial f r) (rand))
+       (drop 300)
+       (take 300)
+       set
+       (map (fn [x] [r x]))))
+
+(def tree (into [] (mapcat fixps) (range 2.5 4.0 0.005)))
+(def width (count tree))
+(def boundary (Math/floor (Math/sqrt width)))
+
+(defn Feigenbaum []
+  [:<>
+   (mb/matrix
+    {:width (quot width boundary)
+     :height (mod width boundary)
+     :channels 2
+     :live false
+     :expr `(fn [emit# i# j#]
+              (apply emit# (nth ~tree (+ (* i# ~boundary) j#) nil)))})
+   (mb/point
+    {:color "#3090FF"
+     :size 1})])
+
+(defn axis
+  ([axis-no] (axis axis-no [0 0 0 0]))
+  ([axis-no origin]
+   [:<>
+    (mb/axis {:axis axis-no
+              :width 2
+              :color "black"
+              :origin origin})
+    (mb/scale  {:divide 10
+                :axis axis-no
+                :origin origin})
+    (mb/ticks  {:width 5
+                :size 15
+                :color "black"})
+    (mb/format {:digits 2
+                :weight "bold"})
+    (mb/label  {:color "red"
+                :zIndex 1})]))
+
+^{::clerk/width :wide}
+(mb/mathbox
+ {:container {:style {:height "1000px" :width "100%"}}}
+ (mb/camera {:position [0 0 2.1]
+             :proxy    true})
+ (mb/layer
+  (mb/cartesian
+   {:range [[2.5 4 0] [0 1 0]]
+    :scale [0.8 0.8 1]}
+   (mb/grid {:width   1
+             :divideX 10
+             :divideY 10})
+   (axis 1)
+   (axis 2 [2.5 0 0 0])
+   (Feigenbaum))))

dev/examples/mathbox/geom.clj

@@ -7,6 +7,7 @@
   (:require [emmy.clerk :as ec]
             [emmy.leva]
             [emmy.env :as e :refer :all]
+            [emmy.matrix]
             [emmy.viewer :as ev]
             [emmy.mathbox.plot :as p]))
 
@@ -15,9 +16,28 @@
 ^{:nextjournal.clerk/visibility {:code :hide :result :hide}}
 (ec/install!)
 
+(defn basis [m]
+  (let [[x y z] (emmy.matrix/transpose m)]
+    (-> [:<>
+         (p/vector {:tip x :arrow-size 3 :color "red"})
+         (p/vector {:tip y :arrow-size 3 :color "green"})
+         (p/vector {:tip z :arrow-size 3 :color "blue"})]
+        (ev/fragment p/scene))))
+
+(ev/with-let [!size {:y 1}]
+  (p/scene
+   (emmy.leva/controls
+    {:atom !size :schema {:y {:min 0 :max 10 :step 0.01}}})
+   (basis
+    (matrix-by-rows
+     [1 0 0]
+     [0 (ev/get !size :y) 0]
+     [1 0 2]))))
+
 (ev/with-let [!size {:size 20 :pos 1}]
-  [:<> (emmy.leva/controls
-        {:atom !size :schema {:size {:min 20 :max 100 :step 1}}})
+  [:<>
+   (emmy.leva/controls
+    {:atom !size :schema {:size {:min 20 :max 100 :step 1}}})
    (p/scene
     (p/point
      {:coords [0.5 -0.5 (ev/get !size :pos)]

dev/examples/simulation/ellipsoid.clj

@@ -82,23 +82,23 @@
 ;;
 ;; Lagrange equations of motion for the ellipsoid:
 
-(def ->tex (comp clerk/tex ->TeX simplify))
-
-(->tex
+(ec/->TeX
  (let [L (L-central-triaxial 'm 'g 'a 'b 'c)
        theta (literal-function 'theta)
        phi (literal-function 'phi)]
-   (((Lagrange-equations L) (up theta phi))
-    't)))
+   (simplify
+    (((Lagrange-equations L) (up theta phi))
+     't))))
 
 ;; And for the sphere:
 
-(->tex
+(ec/->TeX
  (let [L (L-central-triaxial 'm 'g 'r 'r 'r)
        theta (literal-function 'theta)
        phi (literal-function 'phi)]
-   (((Lagrange-equations L) (up theta phi))
-    't)))
+   (simplify
+    (((Lagrange-equations L) (up theta phi))
+     't))))
 
 ;; This is fairly horrifying. This really demands animation, as I bet it looks
 ;; cool, but it's not comprehensible in this form.