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flowFields.py
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flowFields.py
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# -*- coding: utf-8 -*-
"""
Created on Sat Aug 22 19:19:08 2020
@author: Louie Hext
"""
import numpy as np
import random as rand
import matplotlib.pyplot as plt
import time as time
class Ball():
def __init__(self,size,n,max_vel):
self.n=n
self.bound=size
self.max_vel=max_vel
self.pos_x=np.random.uniform(0,size,(n))
self.pos_y=np.random.uniform(0,size,(n))
self.vel_x=np.zeros(n)
self.vel_y=np.zeros(n)
self.acc_x=np.zeros(n)
self.acc_y=np.zeros(n)
self.x_hist=self.pos_x
self.y_hist=self.pos_y
def update(self):
self.pos_x=(self.pos_x+self.vel_x)
self.pos_y=(self.pos_y+self.vel_y)
self.vel_x=(self.vel_x+self.acc_x)/5 #we divide here to have stronger
self.vel_y=(self.vel_y+self.acc_y)/5 #direction without speeding up
self.acc_x=0 #too much
self.acc_y=0
def apply_force(self,fx,fy):
self.acc_x=self.acc_x+fx
self.acc_y=self.acc_y+fy
def speed_check(self):
"""
scales velocity vector such that it has a magnitude less than the
max velocity. Direction is kept the same during scaling
"""
mag=np.zeros((self.n),dtype=bool)
mags=self.vel_x**2+self.vel_y**2
mag=mags>self.max_vel**2
rescaler=mags[mag]/self.max_vel
self.vel_x[mag]=self.vel_x[mag]/rescaler
self.vel_y[mag]=self.vel_y[mag]/rescaler
def edge_check(self):
"""
Applies a torus symmetery, i.e particles loop around
"""
self.pos_x=np.mod(self.pos_x+self.bound,self.bound)
self.pos_y=np.mod(self.pos_y+self.bound,self.bound)
def get_forces(self,vector_x,vector_y):
index_x=np.floor(self.pos_x).astype(int)
index_y=np.floor(self.pos_y).astype(int) #floor as index start at 0
fx=vector_x[index_x,index_y]
fy=vector_y[index_x,index_y]
return fx,fy
def drive(self,vector_x,vector_y,m):
count=0
while count<m:
fx,fy=self.get_forces(vector_x,vector_y)
self.apply_force(fx,fy)
self.update()
self.x_hist=np.vstack([self.x_hist,self.pos_x])
self.y_hist=np.vstack([self.y_hist,self.pos_y])
self.edge_check()
self.speed_check()
count=count+1
return self.x_hist,self.y_hist
def inner_grid_setup(sx,ex,sy,ey,n):
"""
sx= start x, ex = end x...
n= steps inside the inner grid
so returns something like
(0,0) (0,0.5) (0,1)
(0.5,0) (0.5,0.5) (0.5,1)
(1,0) (1,0.5) (1,1)
"""
inner_grid=np.zeros((n,n,2))
x=np.linspace(sx,ex,n)
y=np.linspace(sy,ey,n)
xx,yy=np.meshgrid(x,y)
for i in range(n):
for j in range(n):
inner_grid[i][j][0]=xx[i][j]
inner_grid[i][j][1]=yy[i][j]
return inner_grid
def get_inner_prevals(corners,m,inner_grid):
""" returns the inner values of the grid"""
#dotting corners and displacement vectors
val_a,val_b,val_c,val_d=[inner_grid_val.dot(corner) for inner_grid_val,corner in zip(inner_grid,corners)]
x=np.linspace(0,1,m)
y=np.linspace(0,1,m)
xx,yy=np.meshgrid(x,y)
#interpolation using fade function
ab=val_a+(6*xx**5-15*xx**4+10*xx**3)*(val_b-val_a)
cd=val_c+(6*xx**5-15*xx**4+10*xx**3)*(val_d-val_c)
val=ab+(6*yy**5-15*yy**4+10*yy**3)*(cd-ab)
return val
def perlin(n,m):
"""
n>m (ints)
"""
scale=int(n/m)+1
vectors=np.random.uniform(-1,1,(scale,scale,2)) #grid of random vectors
vectors[-1,:]=vectors[0,:]
vectors[-2,:]=vectors[1,:]
vectors[:,-1]=vectors[:,0]
vectors[:,-2]=vectors[:,1]
data=np.ones((n,n))
a=inner_grid_setup(0,1,0,-1,m) #sets up inner grids
b=inner_grid_setup(-1,0,0,-1,m)
c=inner_grid_setup(0,1,1,0,m)
d=inner_grid_setup(-1,0,1,0,m)
inner_grid=[a,b,c,d]
for i in range(scale-1):
for j in range(scale-1):
corners=[vectors[i][j],vectors[i][j+1],vectors[i+1][j],vectors[i+1][j+1]]
heights=get_inner_prevals(corners, m,inner_grid)
data[i*m:(i+1)*m,j*m:(j+1)*m]=heights
return data
def fractal(n,m,k,plot_result=False):
"""
n>k (ints)
super imposes different frequency perlin noise
"""
maximum=2**n
data=np.zeros((maximum,maximum))
for i in range(k):
temp=perlin(maximum,2**(m-i))*(2**(-(m+i)))
data=data+temp/k
data=data
if plot_result:
plot(maximum,data)
return data
def rotate(xs,ys,angles):
new_xs = np.cos(angles) * (xs) - np.sin(angles) * (ys)
new_ys = np.sin(angles) * (xs) + np.cos(angles) * (ys)
return new_xs, new_ys
def vector_field(data,wildness=25,x_scale=50,y_scale=100):
size=len(data[0])
vector_y=np.ones((size,size))
vector_x=np.zeros((size,size))
angles=2*np.pi*data*wildness
vector_x,vector_y=rotate(vector_x,vector_y,angles)
vector_x=vector_x*x_scale
vector_y=vector_y*y_scale
return vector_x,vector_y
def dipoles(vector_x,vector_y,num,strength):
size=np.shape(vector_x)[0]
x=np.linspace(0,size,size)
y=np.linspace(0,size,size)
xx,yy=np.meshgrid(x,y)
Ex=np.zeros((size,size))
Ey=np.zeros((size,size))
for i in range(num):
px,py=strength*np.random.uniform(-5,5,size=(2,1))
pos_x,pos_y=np.random.uniform(0,size,size=(2,1))
rx=xx-pos_x
ry=yy-pos_y
r=(rx*rx+ry*ry)**0.5
rx_norm=rx/r
ry_norm=ry/r
dot=rx_norm*px+ry_norm*py
ex=(3*dot*rx_norm-px)/r**2
ey=(3*dot*ry_norm-py)/r**2
Ex=Ex+ex
Ey=Ey+ey
return vector_x+Ex,vector_y+Ey
def non_overlap_plot(x,y,c_list,s_list):
x=x.T
y=y.T
fig=plt.figure()
fig.set_size_inches(19.2,10.8)
plt.tick_params(top=False, bottom=False, left=False, right=False,
labelleft=False, labelbottom=False)
ax = plt.gca()
ax.spines['bottom'].set_color('white')
ax.spines['top'].set_color('white')
ax.spines['right'].set_color('white')
ax.spines['left'].set_color('white')
ax.set_aspect(1)
fig.canvas.draw()
x=np.reshape(x,(np.shape(x)[0]*np.shape(x)[1]))
y=np.reshape(y,(np.shape(y)[0]*np.shape(y)[1]))
size=max((max(x),max(y)))
s_list=size/s_list
count=0
alpha=[0.15,0.2,0.3,0.4]
while count<len(x):
color=rand.choice(c_list)
t=rand.choice(s_list)
ty=t
step=int(rand.randint(count, len(x))/10)
temp_x=x[count:count+step]
temp_y=y[count:count+step]
temp_x=(np.around(temp_x/t))*t
temp_y=(np.around(temp_y/ty))*ty
points=[(temp_x[i],temp_y[i]) for i in range(len(temp_x))]
points=list(set(points))
temp_x=np.array(points)[:,0]
temp_y=np.array(points)[:,1]
s = ((ax.get_window_extent().width*(t/(0.5*np.pi) ) / (size) * 72./fig.dpi) ** 2)
ax.scatter(temp_x,temp_y,s=s*2,alpha=rand.choice(alpha)/2,color=color,)
ax.patch.set_alpha(0.5)
count=count+step
def plot(n,data,name="test"):
plt.figure()
fig = plt.gcf()
fig.set_size_inches(19.2,10.8)
plt.clf()
plt.axis('off')
ax = fig.add_subplot(1,1,1)
plt.axis('off')
x=np.linspace(0,n,n)
y=np.linspace(0,n,n)
ax.pcolormesh(x, y, data,cmap="Greys")
def plot_flow(x_hist,y_hist,c_list,s_list,saving=False):
"""
This is quite inefficient due to plotting each line seperately. This is needed
if you want matplotlib to apply alpha properly. Will consider changing libraries
"""
plt.figure()
plt.clf()
fig = plt.gcf()
fig.set_size_inches(19.2,10.8)
plt.axis('off')
x_hist=x_hist.transpose()
y_hist=y_hist.transpose()
plt.style.use("default")
for i in range(len(x_hist)):
count=0
while count<len(x_hist[i]):
color=rand.choice(c_list)
s=rand.choice(s_list)
step=rand.randint(count, len(x_hist[i]))
temp_x=x_hist[i][count:count+step]
temp_y=y_hist[i][count:count+step]
plt.scatter(temp_x,temp_y,s=s*2.5,alpha=0.2,color=color,)
count=count+step
plt.show()
if saving:
name=str(rand.random())
plt.savefig(name,dpi=600)
def plot_line(data,y,saving=False):
plt.style.use('dark_background')
plt.figure()
plt.clf()
fig = plt.gcf()
fig.set_size_inches(19.2,10.8)
plt.axis('off')
for i in range(len(data)):
plt.plot(data[i],y,color="white",alpha=0.25)
if saving:
name=str(rand.random())
plt.savefig("line " + name,dpi=600)
def plot_circle(data,theta,saving=False):
plt.style.use('dark_background')
plt.figure()
plt.clf()
fig = plt.gcf()
fig.set_size_inches(19.2,10.8)
plt.axis('off')
for i in range(len(data)):
x=data[i]*np.cos(theta)
y=data[i]*np.sin(theta)
plt.plot(x,y,color="white",alpha=0.12)
if saving:
name=str(rand.random())
plt.savefig("circle " + name,dpi=600)
def run(n,m,k,balls,updates,max_vel=5,wildness=25,x_scale=500,y_scale=1000,
style="defualt",
c_list=["#007D32","#6BFFA6","#00FC65","#5B8069","#00CC50","#04577A","#53C8FB","#07B1FA","#28627A","#068CC7","white"],
s_list=[100,110,90,85,105,115]):
""" n>k (ints)
"""
s=time.time()
data=fractal(n,m,k)
size=len(data[0])
vector_x,vector_y=vector_field(data,wildness,x_scale,y_scale)
balls=Ball(size=size,n=balls,max_vel=max_vel)
x_hist,y_hist=balls.drive(vector_x, vector_y, updates)
if style=="defualt":
plot_flow(x_hist, y_hist,c_list,s_list)
if style=="mosaic":
non_overlap_plot(x_hist, y_hist,c_list,s_list)
print(time.time()-s)
def run_curl(n,m,k,balls,updates,max_vel=5,wildness=25,x_scale=50,y_scale=100,
dipoles=False,
style="defualt",
c_list=["#007D32","#6BFFA6","#00FC65","#5B8069","#00CC50","#04577A","#53C8FB","#07B1FA","#28627A","#068CC7","white"],
s_list=[100,110,90,85,105,115]):
s=time.time()
pot=fractal(n,m,k)
size=len(pot[0])
vector_x,vector_y=vector_field(pot,wildness,x_scale,y_scale)
x=np.gradient(vector_y,axis=1)
y=-np.gradient(vector_x,axis=0)
if dipoles:
x,y=dipoles(x, y, 8, 100000)
balls=Ball(size=size,n=balls,max_vel=max_vel)
x_hist,y_hist=balls.drive(x, y, updates)
if style=="defualt":
plot_flow(x_hist, y_hist,c_list,s_list)
if style=="mosaic":
non_overlap_plot(x_hist, y_hist,c_list,s_list)
print(time.time()-s)
def run_lines(n,m,k,distortion):
var=fractal(n,m,k)*distortion
size=np.shape(var)[0]
x=np.linspace(0,size,size)
y=np.linspace(0,size,size)
X,Y=np.meshgrid(x,y)
data=var+X
columns=[]
for i in range(np.shape(data)[0]):
temp=data[:,i]
columns.append(temp)
plot_line(columns,y)
def run_circle(n,m,k,distortion):
var=fractal(n,m,k)*distortion
size=np.shape(var)[0]
r=np.linspace(size/9,size,size)
theta=np.linspace(0,1.998*np.pi,size)
R,Theta=np.meshgrid(r,theta)
data=var+R
columns=[]
for i in range(np.shape(data)[0]):
temp=data[:,i]
columns.append(temp)
plot_circle(columns,theta)
if __name__=='__main__':
reds=["white","white","white","#7A2418","#FB8C7D","#FA4932","#7A443D","#C23827"]
black_and_yellow=["black","white","#FCED0D","#FFF200","white","black","black","black","white","white"]
green_and_blue=["#007D32","#6BFFA6","#00FC65","#5B8069","#00CC50","#04577A","#53C8FB","#07B1FA","#28627A","#068CC7","white"]
warm_and_blue=["#1972D1","#D13224","#0ED0D1","#D19124","#17D16A","#5AD1B3","#D18B28"]
blues=["#04577A","#53C8FB","#07B1FA","#28627A","#068CC7","white"]
mono=["grey","black","white"]
big=np.array([190,200,200,400,150,170,100,85,125,1000,80,90,75,])
med=np.array([100,110,90,85,105,115])
small=np.array([100,20,50,65,30,80])
vsmall=np.array([30,20,25,10,15,5])
# run(7,5,4,2000,100,max_vel=5,wildness=25,x_scale=50,y_scale=50,c_list=reds,s_list=vsmall)
run_curl(7,6,3,2000,100,max_vel=5,wildness=25,x_scale=50,y_scale=50,dipoles=False,c_list=reds,s_list=vsmall)
# run_lines(8,7,6,1e5)
# run_circle(8,7,6,1e5)
plt.show()