diff --git a/.gitattributes b/.gitattributes
index dfe0770..eba1110 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -1,2 +1,2 @@
 # Auto detect text files and perform LF normalization
-* text=auto
+* text=auto
\ No newline at end of file
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..f02998d
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1 @@
+.avi
\ No newline at end of file
diff --git a/.vscode/settings.json b/.vscode/settings.json
new file mode 100644
index 0000000..9ee86e7
--- /dev/null
+++ b/.vscode/settings.json
@@ -0,0 +1,6 @@
+{
+    "[python]": {
+        "editor.defaultFormatter": "ms-python.autopep8"
+    },
+    "python.formatting.provider": "none"
+}
\ No newline at end of file
diff --git a/polaired.py b/polaired.py
index ff5c58d..98dda8c 100644
--- a/polaired.py
+++ b/polaired.py
@@ -20,26 +20,6 @@ def rainbow_gradient(num_colors):
     return colors
 colors = rainbow_gradient(nbv)
 
-def status(distances):
-    num_colors = len(distances)
-    colors = []
-    base_color = Color("green")
-    target_color = Color("red")
-    luminance_start = base_color.get_luminance()
-    luminance_end = target_color.get_luminance()
-    for i in range(num_colors):
-        moydist = distances[i]
-        t = i / (num_colors - 1)
-        adjusted_luminance = luminance_start + (luminance_end - luminance_start) * (1 - t) * (moydist - 1) / 18
-        color = Color(rgb=(base_color.rgb[0] * (1 - t) + target_color.rgb[0] * t,
-                           base_color.rgb[1] * (1 - t) + target_color.rgb[1] * t,
-                           base_color.rgb[2] * (1 - t) + target_color.rgb[2] * t))
-        color.set_luminance(adjusted_luminance)
-        hex_code = color.hex_l
-        colors.append(hex_code)
-    return colors
-
-
 U = 1.25 # vitesse m.s-¹
 Wm = 0.3 # distance minimale entre la voiture et celle qui la précède m
 Ws = 0.9 # m
@@ -64,34 +44,24 @@ def position(fposition, newv):
 
 xxold = xxbase.copy()
 
-while(t<tf):
-    plt.figure(1,figsize=[16,9])
+while(t < tf):
+    plt.figure(1, figsize=[16, 9])
     plt.clf()
 
     nb = 360
+    r = np.linspace(1, 1, nb)
+    theta = np.linspace(0, 2 * np.pi, nb)
 
-    r=np.linspace(1,1,nb)
-    theta=np.linspace(0,2*np.pi,nb)
-
-    plt.polar(theta, r)
-    # plt.scatter(1*np.pi, 0.5)
+    plt.polar(theta, r, alpha=0)
 
     dst = distances(xxold)
-    statusc = status(dst)
-    print(statusc)
 
     vt = phi(dst)
-    # print('vitesses : ', vt)
-
     xx = position(xxold, vt)
-    # print('position : ', xx)
 
-    plt.scatter(xx/10*np.pi, y, c=colors)
+    plt.scatter(xx/10 * np.pi, y, c=colors)
 
-    for i in range(len(xx)):
-        plt.plot(xx[i]/10*np.pi, y[i], color=statusc[i])
-
-    plt.title('Vitesse maximale : ' + str(U) + 'm.s-¹\ndistance minimale entre deux voitures : ' + str(Wm) + 'm\nnombre de voitures : ' + str(nbv))
+    plt.title('Vitesse maximale : ' + str(U) + ' m/s\ndistance minimale entre deux voitures : ' + str(Wm) + ' m\nnombre de voitures : ' + str(nbv))
     plt.draw()
     plt.pause(0.00001)
     t += dt
diff --git a/polairedc.py b/polairedc.py
new file mode 100644
index 0000000..f870f64
--- /dev/null
+++ b/polairedc.py
@@ -0,0 +1,125 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import time
+from colour import Color
+
+t0 = 0
+tf = 100
+dt = 0.5
+t = t0
+
+nbv = 20
+
+def rainbow_gradient(num_colors):
+    colors = []
+    base_color = Color("violet")
+    gradient = list(base_color.range_to(Color("red"), num_colors))
+    for color in gradient:
+        hex_code = color.hex_l
+        colors.append(hex_code)
+    return colors
+colors = rainbow_gradient(nbv)
+
+def status(distances):
+    num_colors = len(distances)
+    colors = []
+    base_color = Color("green")
+    target_color = Color("red")
+    luminance_start = base_color.get_luminance()
+    luminance_end = target_color.get_luminance()
+    for i in range(num_colors):
+        moydist = distances[i]
+        t = i / (num_colors - 1)
+        adjusted_luminance = luminance_start + (luminance_end - luminance_start) * (1 - t) * (moydist - 1) / 18
+        color = Color(rgb=(base_color.rgb[0] * (1 - t) + target_color.rgb[0] * t,
+                           base_color.rgb[1] * (1 - t) + target_color.rgb[1] * t,
+                           base_color.rgb[2] * (1 - t) + target_color.rgb[2] * t))
+        color.set_luminance(adjusted_luminance)
+        hex_code = color.hex_l
+        colors.append(hex_code)
+    return colors
+
+
+U = 1.25 # vitesse m.s-¹
+Wm = 0.3 # distance minimale entre la voiture et celle qui la précède m
+Ws = 0.9 # m
+
+def phi(ww): # prend en entrée la distance entre les deux véhicules
+    PHI = (U*(1 - np.exp(- (ww-Wm)/Ws)))
+    return (ww >= Wm)* PHI  # retourne la vitesse du véhicule
+
+y = np.linspace(1, 1, nbv)
+xxbase = np.linspace(0, 1, nbv)
+
+def distances(fposition):
+    # print('fposition', fposition)
+    dist = np.diff(fposition)
+    inter = fposition[0]+20-fposition[-1]
+    newdist = np.insert(dist, len(dist), inter)
+    return newdist
+
+def position(fposition, newv):
+    newp = fposition + newv * dt
+    return newp
+
+xxold = xxbase.copy()
+
+# while(t<tf):
+#     plt.figure(1,figsize=[16,9])
+#     plt.clf()
+
+#     nb = 360
+
+#     r=np.linspace(1,1,nb)
+#     theta=np.linspace(0,2*np.pi,nb)
+
+#     plt.polar(theta, r)
+#     # plt.scatter(1*np.pi, 0.5)
+
+#     dst = distances(xxold)
+#     statusc = status(dst)
+#     print(statusc)
+
+#     vt = phi(dst)
+#     # print('vitesses : ', vt)
+
+#     xx = position(xxold, vt)
+#     # print('position : ', xx)
+
+#     plt.scatter(xx/10*np.pi, y, c=colors)
+
+#     for i in range(len(xx)):
+#         plt.plot(xx[i]/10*np.pi, y[i], color=statusc[i])
+
+#     plt.title('Vitesse maximale : ' + str(U) + 'm.s-¹\ndistance minimale entre deux voitures : ' + str(Wm) + 'm\nnombre de voitures : ' + str(nbv))
+#     plt.draw()
+#     plt.pause(0.00001)
+#     t += dt
+#     xxold = xx.copy()
+
+while(t < tf):
+    plt.figure(1, figsize=[16, 9])
+    plt.clf()
+
+    nb = 360
+    r = np.linspace(1, 1, nb)
+    theta = np.linspace(0, 2 * np.pi, nb)
+
+    plt.polar(theta, r, alpha=0)
+
+    dst = distances(xxold)
+    statusc = status(dst)
+
+    vt = phi(dst)
+    xx = position(xxold, vt)
+
+    plt.scatter(xx/10 * np.pi, y, c=colors)
+
+    for i in range(len(xx)-1):
+        plt.plot([xx[i]/10 * np.pi, xx[i+1]/10 * np.pi], [y[i], y[i+1]], color=statusc[i])
+
+    plt.title('Vitesse maximale : ' + str(U) + ' m/s\ndistance minimale entre deux voitures : ' + str(Wm) + ' m\nnombre de voitures : ' + str(nbv))
+    plt.draw()
+    plt.pause(0.00001)
+    t += dt
+    xxold = xx.copy()
diff --git a/resultats/vidéos/20.mkv b/resultats/vidéos/20.mkv
new file mode 100644
index 0000000..b6384a7
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diff --git a/resultats/vidéos/20_fast.mkv b/resultats/vidéos/20_fast.mkv
new file mode 100644
index 0000000..57694ed
Binary files /dev/null and b/resultats/vidéos/20_fast.mkv differ
diff --git a/resultats/vidéos/30.mkv b/resultats/vidéos/30.mkv
new file mode 100644
index 0000000..0d91bb9
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diff --git a/resultats/vidéos/30_fast.mkv b/resultats/vidéos/30_fast.mkv
new file mode 100644
index 0000000..f5f9f04
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