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diff --git a/gipps V2 (modélisation)/gippsV1.py b/gipps V2 (modélisation)/gippsV1.py
new file mode 100644
index 0000000..3836bfb
--- /dev/null
+++ b/gipps V2 (modélisation)/gippsV1.py	
@@ -0,0 +1,133 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import time
+from colour import Color
+import imagesV1 as images
+import imagesV2 as images2
+
+fps = 2
+
+# ===========
+t0 = 0
+tf = 40
+dt = 1
+t = t0
+# ===========
+nbv = 2
+
+"""# ===========       VARIABBLES
+Xn(t) # position au temps t
+Vn(t) # vitesse au temps t
+An(t+Tr) # accel au temps t + Tr
+ln # ?
+k # ?
+m # ?
+"""
+
+# ===========       CONSTANTES
+An = 1.7 # accel max                                          sampled from a normal distribution. N(1.7,0.3²) m/s²
+Bn = -2 * An # frein max                                          equated to - 2An
+Sn =  6.5 # taille de la voiture plus marge                    sampled from a normal distribution. N(6.5,0.3²) m
+Vd = 20.0 # vitesse désirée                                    sampled from a normal distribution. N(20.0,3.2²) m/sec
+Vmin = 1
+# X*n # position fin de freinage (calculable)
+Tr = 2/3 + (2/3)/2 # temps de réaction + sûreté                 (= tau + θ = 2/3 + tau/2)
+# B supposé égal à Bn-1 (si pas égal alors amplifications ??)
+
+
+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 px(tt):             # Avance au cours du temps
+    tt += 1/fps
+    return tt
+
+def vitesseatt(vtold):       # Vitesse qu'il peut réellement atteindre d'un point de vue dynamique
+    value = vtold + 2.5 * An * Tr * ( 1 - (vtold/Vd) ) * np.sqrt( ( 0.025 + (vtold/Vd) ))
+    return value
+    
+
+def vitesseadop(vtold, xxpold):      # Vitesse qu'il est possible d'adopter en connaissant les contraintes de sécurité liées à la présence du véhicule leader
+    dst = np.diff(xxpold)
+    value = Bn * Tr + np.sqrt( ((Bn)**2) * ((Tr)**2) - Bn * ( 2 * dst) - vtold[0] * Tr - ( (xxold[-1])**2 / Bn )  )
+    newvalue = np.insert(value, 1, vtold[1])
+    print('newvalue: ', newvalue)
+    return newvalue
+
+def vitessereelle(t, vtold, xxpold):    # Vitesse du véhicule
+    # t+=t
+    if t==0:
+        vtold[-1] = 0.1
+    elif (t> 0) and (t<=10):     # Accélération du leader
+        a = (Vd - Vmin) / 10
+        vtleader = Vmin + a * t
+        vtold[-1] = vtleader
+    elif (t>= 16) and (t<=20):  # Leader freine
+        a = - (Vd - Vmin) / 10
+        vtleader = Vd + 2 * a * (t - 16)
+        vtold[-1] = vtleader
+    elif (t> 20) and (t<=30):  # Accélération du leader
+        a = (Vd - Vmin) / 10
+        vtleader = Vmin + a * (t-20)
+        vtold[-1] = vtleader
+    else:                   # Leader avance normalement
+        vtold[-1] = Vd
+    
+    vatt = vitesseatt(vtold)
+    vadop = vitesseadop(vtold, xxpold)
+    minimum = np.minimum(vatt, vadop)
+    print('minimum: ', minimum)
+    return minimum
+
+
+
+def position(fposition, newv):
+    newp = fposition + newv * dt
+    return newp
+
+xxbase = np.linspace(-nbv, 1, nbv)
+xxpbase = np.linspace(0, 1, nbv)
+yybase = np.linspace(0, 1, nbv)
+
+xxold = xxbase.copy()
+xxpold = xxpbase.copy()
+vtold = yybase.copy()
+
+while(t<=tf):
+    plt.figure(1,figsize=[16,9])
+    # plt.clf()
+    plt.xlim([-1,41])
+    plt.ylim([-0.5, Vd+1])
+    
+    xx = px(xxold)
+
+    vt = vitessereelle(t, vtold, xxpold)
+
+    xxp = position(xxpold, vt)
+
+    plt.scatter(xx, vt, c=colors)
+
+    plt.plot([0,40],[Vd, Vd], color='k', linestyle='-', linewidth=1)
+    plt.xlabel('temps en s', fontsize = 16)
+    plt.ylabel('vitesse en m.s-¹', fontsize = 16)
+    plt.xticks(fontsize = 14)
+    plt.yticks(fontsize = 14)
+    # plt.title('Vitesse maximale désirée\nvitesse du leader : ' + str(Vd) + 'm.s-¹\ndistance entre deux voitures : ' + str(np.diff(xxpold)) + 'm\n\nTemps : ' + str(t))
+    plt.draw()
+    if t == tf:
+        plt.savefig('gipps V2 (modélisation)/V1.png')
+    plt.pause(0.00001)
+    t += dt/fps
+    xxold = xx.copy()
+    xxpold = xxp.copy()
+    vtold = vt.copy()
+
+# images.merge()
+# images2.merge(fps)
\ No newline at end of file
diff --git a/gipps V2 (modélisation)/gippsV2.py b/gipps V2 (modélisation)/gippsV2.py
new file mode 100644
index 0000000..c189a3a
--- /dev/null
+++ b/gipps V2 (modélisation)/gippsV2.py	
@@ -0,0 +1,132 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import time
+from colour import Color
+import imagesV2 as images
+
+fps = 4
+
+# ===========
+t0 = 0
+tf = 40
+dt = 1
+t = t0
+# ===========
+nbv = 2
+
+"""# ===========       VARIABBLES
+Xn(t) # position au temps t
+Vn(t) # vitesse au temps t
+An(t+Tr) # accel au temps t + Tr
+ln # ?
+k # ?
+m # ?
+"""
+
+# ===========       CONSTANTES
+An = 1.7 # accel max                                          sampled from a normal distribution. N(1.7,0.3²) m/s²
+Bn = -2 * An # frein max                                          equated to - 2An
+Sn =  6.5 # taille de la voiture plus marge                    sampled from a normal distribution. N(6.5,0.3²) m
+Vd = 20.0 # vitesse désirée                                    sampled from a normal distribution. N(20.0,3.2²) m/sec
+Vmin = 1
+# X*n # position fin de freinage (calculable)
+Tr = 2/3 + (2/3)/2 # temps de réaction + sûreté                 (= tau + θ = 2/3 + tau/2)
+# B supposé égal à Bn-1 (si pas égal alors amplifications ??)
+
+
+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 px(tt):             # Avance au cours du temps
+    tt += 1/fps
+    return tt
+
+def vitesseatt(vtold):       # Vitesse qu'il peut réellement atteindre d'un point de vue dynamique
+    value = vtold + 2.5 * An * Tr * ( 1 - (vtold/Vd) ) * np.sqrt( ( 0.025 + (vtold/Vd) ))
+    return value
+    
+
+def vitesseadop(vtold, xxpold):      # Vitesse qu'il est possible d'adopter en connaissant les contraintes de sécurité liées à la présence du véhicule leader
+    dst = np.diff(xxpold)
+    value = Bn * Tr + np.sqrt( ((Bn)**2) * ((Tr)**2) - Bn * ( 2 * dst) - vtold[0] * Tr - ( (xxold[-1])**2 / Bn )  )
+    newvalue = np.insert(value, 1, vtold[1])
+    print('newvalue: ', newvalue)
+    return newvalue
+
+def vitessereelle(t, vtold, xxpold):    # Vitesse du véhicule
+    
+    if t==0:
+        vtold[-1] = 0.1
+    elif (t> 0) and (t<=10):     # Accélération du leader
+        a = (10 - Vmin) / 10
+        vtleader = Vmin + a * t
+        vtold[-1] = vtleader
+    elif (t>= 16) and (t<=20):  # Leader freine
+        a = - (10 - Vmin) / 10
+        vtleader = 10 + 2 * a * (t - 16)
+        vtold[-1] = vtleader
+    elif (t> 20) and (t<=29):  # Accélération du leader
+        a = (Vd - Vmin) / 10
+        vtleader = Vmin + a * (t-19)
+        vtold[-1] = vtleader
+    elif (t> 29) and (t<=40):  # Accélération du leader
+        vtold[-1] = 20
+    else:                   # Leader avance normalement
+        vtold[-1] = 10  
+    
+    vatt = vitesseatt(vtold)
+    vadop = vitesseadop(vtold, xxpold)
+    minimum = np.minimum(vatt, vadop)
+    print('minimum: ', minimum)
+    return minimum
+
+
+
+def position(fposition, newv):
+    newp = fposition + newv * dt
+    return newp
+
+xxbase = np.linspace(-nbv, 1, nbv)
+xxpbase = np.linspace(0, 1, nbv)
+yybase = np.linspace(0, 1, nbv)
+
+xxold = xxbase.copy()
+xxpold = xxpbase.copy()
+vtold = yybase.copy()
+
+while(t<=tf):
+    plt.figure(1,figsize=[16,9])
+    # plt.clf()
+    plt.xlim([-1,41])
+    plt.ylim([-0.5, Vd+1])
+    
+    xx = px(xxold)
+
+    vt = vitessereelle(t, vtold, xxpold)
+
+    xxp = position(xxpold, vt)
+
+    plt.scatter(xx, vt, c=colors)
+
+    plt.plot([0,40],[Vd, Vd], color='k', linestyle='-', linewidth=1)
+    plt.xlabel('temps en s', fontsize = 16)
+    plt.ylabel('vitesse en m.s-¹', fontsize = 16)
+    plt.xticks(fontsize = 14)
+    plt.yticks(fontsize = 14)
+    # plt.title('Vitesse maximale désirée\nvitesse du leader : ' + str(Vd) + 'm.s-¹\ndistance entre deux voitures : ' + str(np.diff(xxpold)) + 'm\n\nTemps : ' + str(t))
+    if t == tf:
+        plt.savefig('gipps V2 (modélisation)/V2-' + str(fps) + '.png')
+    plt.pause(0.0001)
+    t += dt/fps
+    xxold = xx.copy()
+    xxpold = xxp.copy()
+    vtold = vt.copy()
+
+# images.merge(fps)
\ No newline at end of file
diff --git a/gipps V2 (modélisation)/graph.png b/gipps V2 (modélisation)/graph.png
new file mode 100644
index 0000000..0aa4900
Binary files /dev/null and b/gipps V2 (modélisation)/graph.png differ
diff --git a/gipps V2 (modélisation)/graph.py b/gipps V2 (modélisation)/graph.py
new file mode 100644
index 0000000..8469c61
--- /dev/null
+++ b/gipps V2 (modélisation)/graph.py	
@@ -0,0 +1,54 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+# ===========       CONSTANTES
+An = 1.7 # accel max                                          sampled from a normal distribution. N(1.7,0.3²) m/s²
+Bn = -2 * An # frein max                                          equated to - 2An
+Sn =  6.5 # taille de la voiture plus marge                    sampled from a normal distribution. N(6.5,0.3²) m
+Vd = 20.0 # vitesse désirée                                    sampled from a normal distribution. N(20.0,3.2²) m/sec
+# X*n # position fin de freinage (calculable)
+Tr = 2/3 + (2/3)/2 # temps de réaction + sûreté                 (= tau + θ = 2/3 + tau/2)
+# B supposé égal à Bn-1 (si pas égal alors amplifications ??)
+
+
+vv = np.linspace(0, 36, 200)
+
+def vitesseatt(vv):       # Vitesse qu'il peut réellement atteindre d'un point de vue dynamique
+    value = vv + 2.5 * An * Tr * ( 1 - (vv/Vd) ) * np.sqrt( ( 0.025 + (vv/Vd) ))
+    return value
+
+
+def vitesseadop(vv):      # Vitesse qu'il est possible d'adopter en connaissant les contraintes de sécurité liées à la présence du véhicule leader
+    value = 1
+    return value
+
+def vitessereelle(vv):      # Vitesse maximale désirée
+    vatt = vitesseatt(vv)
+    vadop = vitesseadop(vv)
+    return min(vatt, vadop)
+
+def plotter(nb):
+    plt.plot([0,nb],[vitesseatt(nb), vitesseatt(nb)], color='k', linestyle='-', linewidth=1)
+    plt.plot([nb, nb],[0, vitesseatt(nb)], color='k', linestyle='-', linewidth=1)
+    plt.scatter(nb, vitesseatt(nb))
+
+plt.figure(figsize=[16,9])
+plt.xlim([0, 37])
+plt.ylim([0, 35])
+
+plt.plot(vv, vitesseatt(vv), '-', color='red')  #, label="Vitesse qu'il peut réellement atteindre d'un point de vue dynamique"
+# plt.plot(vv, vitesseadop(vv), '-', color='green', label='No mask')
+
+plotter(10)
+plotter(20)
+plotter(30)
+
+# plt.legend(fontsize = 16, loc='upper center')
+# plt.title('Variation de la vitesse de la voiture suivant en fonction de la voiture leader (première partie du modèle de Gipps)')
+plt.xlabel('vitesse de la voiture leader en m.s-¹', fontsize = 16)
+plt.ylabel('vitesse de la voiture qui suit en m.s-¹', fontsize = 16)
+plt.xticks(fontsize = 14)
+plt.yticks(fontsize = 14)
+plt.savefig('gipps V2 (modélisation)/graph.png')
+plt.draw()
+plt.pause(4)
\ No newline at end of file
diff --git a/gipps V2 (modélisation)/imagesV1.py b/gipps V2 (modélisation)/imagesV1.py
new file mode 100644
index 0000000..ded5506
--- /dev/null
+++ b/gipps V2 (modélisation)/imagesV1.py	
@@ -0,0 +1,42 @@
+from PIL import Image
+import os
+import shutil
+
+try:os.remove('gipps/merged.png')
+except:pass
+
+def merge_images(overlay_folder, output_path):
+    overlay_path = f"{overlay_folder}/1.png"
+    overlay = Image.open(overlay_path)
+    result_width, result_height = overlay.size
+    result = Image.new('RGB', (result_width, result_height), color=(255, 255, 255))
+    x, y = 0, 0
+    for i in range(1,40):
+        overlay_path = f"{overlay_folder}/{i}.png"
+        overlay = Image.open(overlay_path)
+        result.paste(overlay, (x, y), overlay)
+    result.save(output_path)
+
+def detrf(folder_path):
+    try:
+        if os.path.exists(folder_path):
+            shutil.rmtree(folder_path)
+            print(f"Folder '{folder_path}' successfully deleted.")
+        else:
+            print(f"Folder '{folder_path}' does not exist.")
+
+        try:
+            os.makedirs(folder_path)
+            print(f"Folder '{folder_path}' successfully created.")
+        except OSError as e:
+            print(f"Error creating folder: {e}")
+
+    except OSError as e:
+        print(f"Error deleting folder: {e}")
+
+def merge():
+    overlay_folder = "gipps/result"
+    output_path = "gipps/merged.png"
+    merge_images(overlay_folder, output_path)
+    detrf('gipps/result')
+    print('merge done')
\ No newline at end of file
diff --git a/gipps V2 (modélisation)/imagesV2.py b/gipps V2 (modélisation)/imagesV2.py
new file mode 100644
index 0000000..6462e0e
--- /dev/null
+++ b/gipps V2 (modélisation)/imagesV2.py	
@@ -0,0 +1,42 @@
+from PIL import Image
+import os
+import shutil
+
+try:os.remove('gipps/merged.png')
+except:pass
+
+def merge_images(overlay_folder, output_path, fps):
+    overlay_path = f"{overlay_folder}/1.png"
+    overlay = Image.open(overlay_path)
+    result_width, result_height = overlay.size
+    result = Image.new('RGB', (result_width, result_height), color=(255, 255, 255))
+    x, y = 0, 0
+    for i in range(1,40*fps):
+        overlay_path = f"{overlay_folder}/{i}.png"
+        overlay = Image.open(overlay_path)
+        result.paste(overlay, (x, y), overlay)
+    result.save(output_path)
+
+def detrf(folder_path):
+    try:
+        if os.path.exists(folder_path):
+            shutil.rmtree(folder_path)
+            print(f"Folder '{folder_path}' successfully deleted.")
+        else:
+            print(f"Folder '{folder_path}' does not exist.")
+
+        try:
+            os.makedirs(folder_path)
+            print(f"Folder '{folder_path}' successfully created.")
+        except OSError as e:
+            print(f"Error creating folder: {e}")
+
+    except OSError as e:
+        print(f"Error deleting folder: {e}")
+
+def merge(fps):
+    overlay_folder = "gipps/result"
+    output_path = "gipps/merged.png"
+    merge_images(overlay_folder, output_path, fps)
+    detrf('gipps/result')
+    print('merge done')
\ No newline at end of file
diff --git a/gipps/merged.png b/gipps/merged.png
deleted file mode 100644
index b28c56a..0000000
Binary files a/gipps/merged.png and /dev/null differ
diff --git a/pipes/dist sécurité.py b/pipes/dist sécurité.py
index 31a6c86..dddef3d 100644
--- a/pipes/dist sécurité.py	
+++ b/pipes/dist sécurité.py	
@@ -2,7 +2,7 @@ import numpy as np
 import matplotlib.pyplot as plt
 import matplotlib.ticker as ticker
 
-vt = 1.25  # 4,5 km/h
+# vt = 1.25  # 4,5 km/h
 Umin = 1  # vitesse m/s
 Umax = 36  # environ 130 km/h
 Wm = 4.23  # longueur du véhicule en m (moyenne française)
@@ -11,7 +11,7 @@ t = np.linspace(0, 15, 400)
 def vitesse(t):
     a = np.where(t <= 10, (Umax - Umin) / 10, - (Umax - Umin) / 10)
     vt = np.where(t <= 10, Umin + a * t, Umax + 2 * a * (t - 10))
-    print('vt: ', vt)
+    # print('vt: ', vt)
     return vt
 
 
diff --git a/pipes/dist sécuritéV2.py b/pipes/dist sécuritéV2.py
new file mode 100644
index 0000000..8014d38
--- /dev/null
+++ b/pipes/dist sécuritéV2.py	
@@ -0,0 +1,54 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import matplotlib.ticker as ticker
+
+# vt = 1.25  # 4,5 km/h
+Umin = 1  # vitesse m/s
+Umax = 36  # environ 130 km/h
+Wm = 4.23  # longueur du véhicule en m (moyenne française)
+t = np.linspace(0, 15, 400)
+
+def vitesse(t):
+    a = np.where(t <= 10, (Umax - Umin) / 10, - (Umax - Umin) / 10)
+    vt = np.where(t <= 10, Umin + a * t, Umax + 2 * a * (t - 10))
+    # print('vt: ', vt)
+    return vt
+
+
+def security(t):
+    vt = np.linspace(1, 36, 400)
+    # ici la vitesse est encore en m/s
+    miles_per_meter = 0.000621371
+    seconds_per_hour = 3600
+    vt = vt * miles_per_meter * seconds_per_hour
+    dist = Wm * (1 + (vt/(16.1/3.6)))
+    # print(dist)
+    return dist
+
+
+fig, ax1 = plt.subplots(figsize=[16, 9])
+ax1.set_xlim([-1, 16])
+ax1.set_xlabel('Temps (s)', fontsize = 16)
+ax1.set_ylabel('Distance de sécurité en m', color='b', fontsize = 16)
+ax1.plot(t, security(t), label='Distance de sécurité', color='b')
+ax1.tick_params(axis='y', labelcolor='blue', labelsize = 14)
+ax1.tick_params(axis='x', labelcolor='black', labelsize = 14)
+
+ax2 = ax1.twinx()
+ax2.set_ylabel('Vitesse de la voiture leader en m/s', color='r', fontsize = 16)
+vitesse_data = np.linspace(1, 36, 400)
+ax2.plot(t, vitesse_data, label='Vitesse de la voiture leader', color='r')
+ax2.tick_params(axis='y', labelcolor='r', labelsize = 14)
+
+
+ax1.set_ylim(-1, 100)
+ax2.set_ylim(-1, 100)
+
+ax1.yaxis.set_major_locator(ticker.LinearLocator(numticks=10))
+ax2.yaxis.set_major_locator(ticker.LinearLocator(numticks=10))
+
+# plt.title(label='Variation de la distance de sécurité en fonction de la vitesse du leader selon le modèle de Pipes', fontsize= 16)
+fig.legend(loc='upper center', fontsize = 16)
+plt.savefig('pipes/dist sécuritésV2.png')
+plt.draw()
+plt.pause(1)
\ No newline at end of file
diff --git a/pipes/dist sécuritésV2.png b/pipes/dist sécuritésV2.png
new file mode 100644
index 0000000..5824c11
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diff --git a/rapport/Titre du rapport.zip b/rapport/Titre du rapport.zip
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index 0000000..e6196d4
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diff --git a/rapport/modélisations/graphique_moedele_trafic_1.png b/rapport/modélisations/graphique_moedele_trafic_1.png
new file mode 100644
index 0000000..4d24514
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diff --git a/rapport/modélisations/phi(ww).png b/rapport/modélisations/phi(ww).png
new file mode 100644
index 0000000..bb396d6
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diff --git a/rapport/modélisations/phi(ww).xcf b/rapport/modélisations/phi(ww).xcf
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index 0000000..ba951e3
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diff --git a/rapport/yoloex/track/labels/voitures.txt b/rapport/yoloex/track/labels/voitures.txt
new file mode 100644
index 0000000..8ca2abf
--- /dev/null
+++ b/rapport/yoloex/track/labels/voitures.txt
@@ -0,0 +1 @@
+2 0.313418 0.484872 0.29448 0.307006
diff --git a/rapport/yoloex/track/voitures.jpg b/rapport/yoloex/track/voitures.jpg
new file mode 100644
index 0000000..7fea4c9
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diff --git a/rapport/yoloex/voitures.jpg b/rapport/yoloex/voitures.jpg
new file mode 100644
index 0000000..14ba3d4
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diff --git a/test/model.py b/test/model.py
index f3ee815..6cc2702 100644
--- a/test/model.py
+++ b/test/model.py
@@ -31,15 +31,27 @@ def position(fposition):
 
 xxold = xxbase.copy()
 
-while(t<tf):
-    plt.figure(1,figsize=[16,9])
-    plt.clf()
-    plt.xlim([-1,10])
+while(t<=tf):
+    plt.figure(1,figsize=[12,5])
+    # plt.clf()
+    plt.xlim([-1,30])
+    plt.ylim([-1, 21])
     xx = position(xxold)
     color = ['#ff0000', '#ff5300', '#ffa500', '#ffd200', '#ffff00', '#80c000', '#008000', '#004080', '#0000ff', '#2600c1', '#4b0082']
-    plt.scatter(xx, y, c=color)
+
+    # plt.plot([0,20],[t, t], color='k', linestyle='-', linewidth=1)
+
+    plt.scatter(xx, np.linspace(t, t, 11), c=color)
+
+    
+    plt.xlabel('distance w  en m', )
+    plt.ylabel('temps en s')
+    # plt.title("Modélisation de l'évolution de la distance entre les voitures\n\nau temps t = " + str(t) + 's')
+
+
     plt.draw()
-    # plt.savefig(str(t)+'.png')
+    if t == 20:
+        plt.savefig('test/model/frame_' + str(t)+'.png')
     plt.pause(0.2)    
     t += dt
-    xxold = xx.copy()
+    xxold = xx.copy()
\ No newline at end of file
diff --git a/test/model/frame_20.png b/test/model/frame_20.png
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index 0000000..f5da7d6
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diff --git a/test/model/frame_20_.png b/test/model/frame_20_.png
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diff --git a/test/model/frame_20_stryied.png b/test/model/frame_20_stryied.png
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index 0000000..49c0a1b
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diff --git a/test/phi(ww).png b/test/phi(ww).png
index bb396d6..d641dba 100644
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diff --git a/test/polaired.py b/test/polaired.py
index 98dda8c..d22a892 100644
--- a/test/polaired.py
+++ b/test/polaired.py
@@ -5,7 +5,7 @@ from colour import Color
 
 t0 = 0
 tf = 100
-dt = 0.5
+dt = 0.25
 t = t0
 
 nbv = 20
@@ -45,13 +45,18 @@ def position(fposition, newv):
 xxold = xxbase.copy()
 
 while(t < tf):
-    plt.figure(1, figsize=[16, 9])
+    plt.figure(1, figsize=[12, 16])
     plt.clf()
 
     nb = 360
     r = np.linspace(1, 1, nb)
     theta = np.linspace(0, 2 * np.pi, nb)
 
+    ax = plt.subplot(111, polar=True)
+
+    ax.set_xticklabels([])
+    ax.set_yticklabels([])
+
     plt.polar(theta, r, alpha=0)
 
     dst = distances(xxold)
@@ -61,8 +66,12 @@ while(t < tf):
 
     plt.scatter(xx/10 * np.pi, y, c=colors)
 
-    plt.title('Vitesse maximale : ' + str(U) + ' m/s\ndistance minimale entre deux voitures : ' + str(Wm) + ' m\nnombre de voitures : ' + str(nbv))
+    # plt.title("Modélisation de l'évolution de la distance entre les voitures (périodique)\n\nnombre de voiture : "+ str(nbv) +"\n\nau temps t = " + str(t) + 's\n')
+    plt.grid(False)
+
     plt.draw()
+    plt.savefig('test/polaired_nbv=20/frame_' + str(t)+'.png')
     plt.pause(0.00001)
     t += dt
+
     xxold = xx.copy()
\ No newline at end of file
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