fix hopf fibration pov file missing bug

README.md

@@ -1,3 +1,3 @@
 # A Tour in the Wonderland of Math with Python
 
-[![CI](https://github.com/neozhaoliang/pywonderland/actions/workflows/test.yaml/badge.svg)](https://github.com/neozhaoliang/pywonderland/actions/workflows/test.yaml)
+[![CI](https://github.com/neozhaoliang/pywonderland/actions/workflows/test.yaml/badge.svg)](https://github.com/neozhaoliang/pywonderland/actions/workflows/test.yaml)

src/cftp/README.md

@@ -3,5 +3,5 @@
 1. [Blog post](https://possiblywrong.wordpress.com/2018/02/23/coupling-from-the-past/) by Possibly Wrong.
 2. Wilson's paper "Mixing times of lozenge tiling and card shuffling Markv chains".
 3. Häggström's book "Markov chains and algorithmic applications"
-4. Book by David Asher Levin, Elizabeth Lee Wilmer, and Yuval Peres "Markov chains and mixing times".
+4. "Markov chains and mixing times". Book by David Asher Levin, Elizabeth Lee Wilmer, and Yuval Peres.
 5. [Markov Chain Algorithms for Planar Lattice Structures](https://www.researchgate.net/publication/2455641_Markov_Chain_Algorithms_for_Planar_Lattice_Structures).

src/misc/Hopf_Fibration.ipynb

@@ -42,7 +42,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "To visualize the Hopf fibration we want to choose some points on the 2-sphere $S^2$, draw their fibers and and see what they look like. Since these fibers lie in the 4d space we cannot see them directly, but if we project them to 3d space using the [stereographic projection](https://en.wikipedia.org/wiki/Stereographic_projection) then some remarkable structure appears. The fibers are projected to circles in 3d space (one of which in a line, comes from the fiber through infinity), any two such circles are linked with each other and the line passes through all circles. The 3d space is filled with nested tori made of linking Villarceau circles, each tori is the preimage of a circle of latitude of the 2-sphere. \n",
+    "To visualize the Hopf fibration, we will choose some points on the 2-sphere $S^2$, draw their fibers and and see what they look like. Since these fibers lie in the 4d space we cannot see them directly, but if we project them to 3d space using the [stereographic projection](https://en.wikipedia.org/wiki/Stereographic_projection) then some remarkable structure appears. The fibers are projected to circles in 3d space (one of which in a line, comes from the fiber through infinity), any two such circles are linked with each other and the line passes through all circles. The 3d space is filled with nested tori made of linking Villarceau circles, each tori is the preimage of a circle of latitude of the 2-sphere. \n",
     "\n",
     "So our plan is:\n",
     "\n",
@@ -360,7 +360,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.10"
+   "version": "3.10.12"
   },
   "latex_envs": {
    "LaTeX_envs_menu_present": true,

src/misc/hopf_fibration.pov

@@ -0,0 +1,52 @@
+#version 3.7;
+
+global_settings {
+    assumed_gamma 2.2
+    max_trace_level 10
+}
+
+#declare TubeThickness = 0.05;
+
+#macro Torus(center, rad, mat, col)
+    torus {
+        rad, TubeThickness
+        texture {
+            pigment {
+                color col
+            }
+            finish {
+                ambient 0.4
+                diffuse 0.5
+                specular 0.6
+                roughness 0.1
+                reflection 0
+            }
+        }
+        matrix <mat[0].x, mat[0].y, mat[0].z,
+                mat[1].x, mat[1].y, mat[1].z,
+                mat[2].x, mat[2].y, mat[2].z,
+                       0,        0,        0>
+        translate center
+    }
+#end
+
+union {
+    #include "torus-data.inc"
+}
+
+camera {
+    location <0, 0, 1> * 9
+    look_at <0, 0, 0>
+    right x*image_width/image_height
+    up y
+    sky y
+}
+
+light_source {
+    <0, 1, 1> * 100
+    color rgb 1
+    area_light
+    x*32, z*32, 5, 5
+    adaptive 1
+    jitter
+}

src/misc/lorenz.py

@@ -30,11 +30,7 @@ def derivative(point, t):
 
 fig = plt.figure(figsize=(6.4, 4.8), dpi=100)
 ax = fig.add_axes(
-    [0, 0, 1, 1],
-    projection="3d",
-    xlim=(-25, 25),
-    ylim=(-35, 35),
-    zlim=(5, 55)
+    [0, 0, 1, 1], projection="3d", xlim=(-25, 25), ylim=(-35, 35), zlim=(5, 55)
 )
 ax.set_box_aspect((1, 1, 1))
 ax.view_init(30, 0)
@@ -90,5 +86,5 @@ def animate(i):
     dpi=200,
     bitrate=1000,
     codec="libx264",
-    extra_args=["-crf", "10"],
+    extra_args=["-crf", "10", "-pix_fmt", "yuv420p"],
 )

src/misc/modulargroup.py

@@ -114,10 +114,8 @@ class HyperbolicDrawing(cairo.Context):
     """
 
     def set_axis(self, **kwargs):
-        surface = self.get_target()
-        width = surface.get_width()
-        height = surface.get_height()
-
+        width = kwargs.get("width", 800)
+        height = kwargs.get("height", 400)
         xlim = kwargs.get("xlim", [-2, 2])
         x_min, x_max = xlim
         ylim = kwargs.get("ylim", [0, 2])
@@ -183,9 +181,11 @@ def main(width, height, depth, xlim=None, ylim=None):
         xlim = [-2, 2]
     if ylim is None:
         ylim = [0, 2]
-    surface = cairo.ImageSurface(cairo.FORMAT_RGB24, width, height)
+    surface = cairo.SVGSurface("modulargroup.svg", width, height)
     ctx = HyperbolicDrawing(surface)
-    ctx.set_axis(xlim=xlim, ylim=ylim, background_color=(1, 1, 1))
+    ctx.set_axis(
+        width=width, height=height, xlim=xlim, ylim=ylim, background_color=(1, 1, 1)
+    )
     ctx.set_line_join(2)
     # draw the x-axis
     ctx.move_to(xlim[0], 0)
@@ -207,11 +207,13 @@ def main(width, height, depth, xlim=None, ylim=None):
             triangle, facecolor=fc_color, linewidth=0.04 / (len(word) + 1)
         )
 
-    surface.write_to_png("modulargroup.png")
+    surface.finish()
 
-    surface = cairo.ImageSurface(cairo.FORMAT_RGB24, width, height)
+    surface = cairo.SVGSurface("cayleygraph.svg", width, height)
     ctx = HyperbolicDrawing(surface)
-    ctx.set_axis(xlim=xlim, ylim=ylim, background_color=(1, 1, 1))
+    ctx.set_axis(
+        width=width, height=height, xlim=xlim, ylim=ylim, background_color=(1, 1, 1)
+    )
     ctx.set_line_join(2)
     # draw the x-axis
     ctx.move_to(xlim[0], 0)
@@ -237,7 +239,7 @@ def main(width, height, depth, xlim=None, ylim=None):
             linewidth=0.02 / (1 + len(word)),
         )
 
-    surface.write_to_png("cayley_graph.png")
+    surface.finish()
 
 
 if __name__ == "__main__":