diff --git a/slides/cours_19.md b/slides/cours_19.md
index 9fd0952c1e98e0e911854b90d595a9474f1e9a61..6041002b7a90630f37b81e26350c4684e0d7943f 100644
--- a/slides/cours_19.md
+++ b/slides/cours_19.md
@@ -358,45 +358,27 @@ Son équivalent tri-dimensionnel est l'octree (chaque noeud a 8 enfants ou aucun
::: columns
-:::: column
+:::: {.column width=30%}
-## Comment représenter l'image?
+## Comment représenter l'image
::::
-:::: column
+:::: {.column width=70%}
+
+## Sous la forme d'un arbre quaternaire?
. . .
-```{.mermaid format=pdf width=400 loc=figs/}
-graph TD;
- id0(( ))-->id1((0));
- id0-->id2(( ));
- id0-->id3(( ));
- id0-->id4(( ));
- id2-->id5(( ))
- id2-->id6((1))
- id2-->id7((1))
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- id3-->id9((1))
- id3-->id10((1))
- id3-->id11((0))
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- id4-->id15((1))
- id4-->id16(( ))
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- id16-->id21((1))
- id16-->id22((1))
- id16-->id23((1))
- id16-->id24((0))
-```
+
+
+**Économie?**
+
+. . .
+
+Image 64 pixels, arbre 25 neouds.
::::
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diff --git a/slides/figs/quad_img.svg b/slides/figs/quad_img.svg
new file mode 100644
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+<title>sd3</title>
+<ellipse fill="none" stroke="#000000" cx="495" cy="-90" rx="27" ry="18"/>
+<text text-anchor="middle" x="495" y="-85.8" font-family="Times,serif" font-size="14.00" fill="#000000">1</text>
+</g>
+<!-- ig1->sd3 -->
+<g id="edge10" class="edge">
+<title>ig1->sd3</title>
+<path fill="none" stroke="#000000" d="M495,-143.8314C495,-136.131 495,-126.9743 495,-118.4166"/>
+<polygon fill="#000000" stroke="#000000" points="498.5001,-118.4132 495,-108.4133 491.5001,-118.4133 498.5001,-118.4132"/>
+</g>
+<!-- ig3 -->
+<g id="node12" class="node">
+<title>ig3</title>
+<ellipse fill="none" stroke="#000000" cx="567" cy="-90" rx="27" ry="18"/>
+<text text-anchor="middle" x="567" y="-85.8" font-family="Times,serif" font-size="14.00" fill="#000000">0</text>
+</g>
+<!-- ig1->ig3 -->
+<g id="edge11" class="edge">
+<title>ig1->ig3</title>
+<path fill="none" stroke="#000000" d="M510.2693,-146.7307C520.197,-136.803 533.3153,-123.6847 544.4363,-112.5637"/>
+<polygon fill="#000000" stroke="#000000" points="547.1564,-114.7933 551.7527,-105.2473 542.2067,-109.8436 547.1564,-114.7933"/>
+</g>
+<!-- id3 -->
+<g id="node13" class="node">
+<title>id3</title>
+<ellipse fill="none" stroke="#000000" cx="639" cy="-90" rx="27" ry="18"/>
+<text text-anchor="middle" x="639" y="-85.8" font-family="Times,serif" font-size="14.00" fill="#000000">1</text>
+</g>
+<!-- ig1->id3 -->
+<g id="edge12" class="edge">
+<title>ig1->id3</title>
+<path fill="none" stroke="#000000" d="M516.8705,-151.0647C541.2222,-138.8889 580.762,-119.119 608.2285,-105.3858"/>
+<polygon fill="#000000" stroke="#000000" points="610.0165,-108.4049 617.3955,-100.8022 606.886,-102.1439 610.0165,-108.4049"/>
+</g>
+<!-- sg4 -->
+<g id="node14" class="node">
+<title>sg4</title>
+<ellipse fill="none" stroke="#000000" cx="711" cy="-90" rx="27" ry="18"/>
+<text text-anchor="middle" x="711" y="-85.8" font-family="Times,serif" font-size="14.00" fill="#000000">1</text>
+</g>
+<!-- id1->sg4 -->
+<g id="edge13" class="edge">
+<title>id1->sg4</title>
+<path fill="none" stroke="#000000" d="M767.7307,-146.7307C757.803,-136.803 744.6847,-123.6847 733.5637,-112.5637"/>
+<polygon fill="#000000" stroke="#000000" points="735.7933,-109.8436 726.2473,-105.2473 730.8436,-114.7933 735.7933,-109.8436"/>
+</g>
+<!-- sd4 -->
+<g id="node15" class="node">
+<title>sd4</title>
+<ellipse fill="none" stroke="#000000" cx="783" cy="-90" rx="27" ry="18"/>
+<text text-anchor="middle" x="783" y="-85.8" font-family="Times,serif" font-size="14.00" fill="#000000">0</text>
+</g>
+<!-- id1->sd4 -->
+<g id="edge14" class="edge">
+<title>id1->sd4</title>
+<path fill="none" stroke="#000000" d="M783,-143.8314C783,-136.131 783,-126.9743 783,-118.4166"/>
+<polygon fill="#000000" stroke="#000000" points="786.5001,-118.4132 783,-108.4133 779.5001,-118.4133 786.5001,-118.4132"/>
+</g>
+<!-- ig4 -->
+<g id="node16" class="node">
+<title>ig4</title>
+<ellipse fill="none" stroke="#000000" cx="855" cy="-90" rx="27" ry="18"/>
+<text text-anchor="middle" x="855" y="-85.8" font-family="Times,serif" font-size="14.00" fill="#000000">1</text>
+</g>
+<!-- id1->ig4 -->
+<g id="edge15" class="edge">
+<title>id1->ig4</title>
+<path fill="none" stroke="#000000" d="M798.2693,-146.7307C808.197,-136.803 821.3153,-123.6847 832.4363,-112.5637"/>
+<polygon fill="#000000" stroke="#000000" points="835.1564,-114.7933 839.7527,-105.2473 830.2067,-109.8436 835.1564,-114.7933"/>
+</g>
+<!-- id4 -->
+<g id="node17" class="node">
+<title>id4</title>
+<ellipse fill="none" stroke="#000000" cx="927" cy="-90" rx="27" ry="18"/>
+<text text-anchor="middle" x="927" y="-85.8" font-family="Times,serif" font-size="14.00" fill="#000000"> </text>
+</g>
+<!-- id1->id4 -->
+<g id="edge16" class="edge">
+<title>id1->id4</title>
+<path fill="none" stroke="#000000" d="M804.8705,-151.0647C829.2222,-138.8889 868.762,-119.119 896.2285,-105.3858"/>
+<polygon fill="#000000" stroke="#000000" points="898.0165,-108.4049 905.3955,-100.8022 894.886,-102.1439 898.0165,-108.4049"/>
+</g>
+<!-- sg5 -->
+<g id="node18" class="node">
+<title>sg5</title>
+<ellipse fill="none" stroke="#000000" cx="27" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">0</text>
+</g>
+<!-- sg2->sg5 -->
+<g id="edge17" class="edge">
+<title>sg2->sg5</title>
+<path fill="none" stroke="#000000" d="M115.6918,-77.1278C98.6445,-65.763 73.5981,-49.0654 54.4656,-36.3104"/>
+<polygon fill="#000000" stroke="#000000" points="56.4031,-33.3956 46.1411,-30.7607 52.5201,-39.2199 56.4031,-33.3956"/>
+</g>
+<!-- sd5 -->
+<g id="node19" class="node">
+<title>sd5</title>
+<ellipse fill="none" stroke="#000000" cx="99" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="99" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">1</text>
+</g>
+<!-- sg2->sd5 -->
+<g id="edge18" class="edge">
+<title>sg2->sd5</title>
+<path fill="none" stroke="#000000" d="M126.2854,-72.5708C122.0403,-64.0807 116.8464,-53.6929 112.1337,-44.2674"/>
+<polygon fill="#000000" stroke="#000000" points="115.237,-42.6477 107.6343,-35.2687 108.976,-45.7782 115.237,-42.6477"/>
+</g>
+<!-- ig5 -->
+<g id="node20" class="node">
+<title>ig5</title>
+<ellipse fill="none" stroke="#000000" cx="171" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="171" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">1</text>
+</g>
+<!-- sg2->ig5 -->
+<g id="edge19" class="edge">
+<title>sg2->ig5</title>
+<path fill="none" stroke="#000000" d="M143.7146,-72.5708C147.9597,-64.0807 153.1536,-53.6929 157.8663,-44.2674"/>
+<polygon fill="#000000" stroke="#000000" points="161.024,-45.7782 162.3657,-35.2687 154.763,-42.6477 161.024,-45.7782"/>
+</g>
+<!-- id5 -->
+<g id="node21" class="node">
+<title>id5</title>
+<ellipse fill="none" stroke="#000000" cx="243" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="243" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">0</text>
+</g>
+<!-- sg2->id5 -->
+<g id="edge20" class="edge">
+<title>sg2->id5</title>
+<path fill="none" stroke="#000000" d="M154.3082,-77.1278C171.3555,-65.763 196.4019,-49.0654 215.5344,-36.3104"/>
+<polygon fill="#000000" stroke="#000000" points="217.4799,-39.2199 223.8589,-30.7607 213.5969,-33.3956 217.4799,-39.2199"/>
+</g>
+<!-- sg6 -->
+<g id="node22" class="node">
+<title>sg6</title>
+<ellipse fill="none" stroke="#000000" cx="819" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="819" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">1</text>
+</g>
+<!-- id4->sg6 -->
+<g id="edge21" class="edge">
+<title>id4->sg6</title>
+<path fill="none" stroke="#000000" d="M907.6918,-77.1278C890.6445,-65.763 865.5981,-49.0654 846.4656,-36.3104"/>
+<polygon fill="#000000" stroke="#000000" points="848.4031,-33.3956 838.1411,-30.7607 844.5201,-39.2199 848.4031,-33.3956"/>
+</g>
+<!-- sd6 -->
+<g id="node23" class="node">
+<title>sd6</title>
+<ellipse fill="none" stroke="#000000" cx="891" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="891" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">1</text>
+</g>
+<!-- id4->sd6 -->
+<g id="edge22" class="edge">
+<title>id4->sd6</title>
+<path fill="none" stroke="#000000" d="M918.2854,-72.5708C914.0403,-64.0807 908.8464,-53.6929 904.1337,-44.2674"/>
+<polygon fill="#000000" stroke="#000000" points="907.237,-42.6477 899.6343,-35.2687 900.976,-45.7782 907.237,-42.6477"/>
+</g>
+<!-- ig6 -->
+<g id="node24" class="node">
+<title>ig6</title>
+<ellipse fill="none" stroke="#000000" cx="963" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="963" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">1</text>
+</g>
+<!-- id4->ig6 -->
+<g id="edge23" class="edge">
+<title>id4->ig6</title>
+<path fill="none" stroke="#000000" d="M935.7146,-72.5708C939.9597,-64.0807 945.1536,-53.6929 949.8663,-44.2674"/>
+<polygon fill="#000000" stroke="#000000" points="953.024,-45.7782 954.3657,-35.2687 946.763,-42.6477 953.024,-45.7782"/>
+</g>
+<!-- id6 -->
+<g id="node25" class="node">
+<title>id6</title>
+<ellipse fill="none" stroke="#000000" cx="1035" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="1035" y="-13.8" font-family="Times,serif" font-size="14.00" fill="#000000">0</text>
+</g>
+<!-- id4->id6 -->
+<g id="edge24" class="edge">
+<title>id4->id6</title>
+<path fill="none" stroke="#000000" d="M946.3082,-77.1278C963.3555,-65.763 988.4019,-49.0654 1007.5344,-36.3104"/>
+<polygon fill="#000000" stroke="#000000" points="1009.4799,-39.2199 1015.8589,-30.7607 1005.5969,-33.3956 1009.4799,-39.2199"/>
+</g>
+</g>
+</svg>
\ No newline at end of file
diff --git a/slides/graphviz/quad_img.dot b/slides/graphviz/quad_img.dot
new file mode 100644
index 0000000000000000000000000000000000000000..9695b62daae48f7bbae6cde539d996b808d614ec
--- /dev/null
+++ b/slides/graphviz/quad_img.dot
@@ -0,0 +1,34 @@
+digraph G {
+ 0 [label=" "]
+ sg1 [label="0"]
+ sd1 [label=" "]
+ ig1 [label=" "]
+ id1 [label=" "]
+ sg2 [label=" "]
+ sd2 [label="1"]
+ ig2 [label="1"]
+ id2 [label="1"]
+ sg3 [label="1"]
+ sd3 [label="1"]
+ ig3 [label="0"]
+ id3 [label="1"]
+ sg4 [label="1"]
+ sd4 [label="0"]
+ ig4 [label="1"]
+ id4 [label=" "]
+ sg5 [label="0"]
+ sd5 [label="1"]
+ ig5 [label="1"]
+ id5 [label="0"]
+ sg6 [label="1"]
+ sd6 [label="1"]
+ ig6 [label="1"]
+ id6 [label="0"]
+
+ 0->{sg1, sd1, ig1, id1}
+ sd1->{sg2, sd2, ig2, id2}
+ ig1->{sg3, sd3, ig3, id3}
+ id1->{sg4, sd4, ig4, id4}
+ sg2->{sg5, sd5, ig5, id5}
+ id4->{sg6, sd6, ig6, id6}
+}