Implementation of semi random motion in 2 dimensions.

demo.py

import pygame
import math
import time
import drunk
import random
width=1000
height=1000
padding = 10
screenColor=(0,0,0)
lineColor=(255,255,255)
screen=pygame.display.set_mode((width+padding,height+padding))
start=time.time()

drunkards = [drunk.drunkard((500,500),420),
            drunk.drunkard((500,500),420,jerk=5),
            drunk.drunkard((500,500),210,jerk=10),
            drunk.drunkard((500,500),210,jerk=10,contained=False)]
            
for k in range(100):
    drunkards.append(drunk.drunkard((500,500),420+160*(random.random()-1),jerk = random.choice([1,2,3,4,5,6,7]),contained=random.choice([True,False])))

points = [ drunkard.nextPosition() for drunkard in drunkards ]

while True:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            pygame.quit()
        if event.type == pygame.KEYDOWN:
            pass
            #if event.key == pygame.K_LEFT:
        if event.type == pygame.KEYUP:
            pass
            #if event.key == pygame.K_LEFT:
    screen.fill(screenColor)
    nextPoints = [ drunkard.nextPosition() for drunkard in drunkards ]
    for a,b in zip(points,nextPoints):
        pygame.draw.line(screen, (255,255,255), a,b)
    points = nextPoints
    pygame.display.flip()
    time.sleep(0.05)

filename = input("FileName:")
pygame.image.save(screen, filename+".PNG")

drunk.py

import os

def fairCoin():
    return os.urandom(1)[0] >= 128

def dist(a,b):
    return sum((i-j)**2 for i,j in zip(a,b))**0.5

def mag(a):
    return dist(a,(0,0))

def dot(a,b):
    return sum([i*j for i,j in zip(a,b)])

def cos(a,b):
    return dot(a,b)/(mag(a)*mag(b))

def proj(a,b):
    return mag(a)*cos(a,b)

def scaleTo(s,a):
    m = mag(a)
    return [s*k/m for k in a]

class drunkard:
    def __init__(self,origin,radius,jerk=1,contained = True):
        self.vmax = int(radius/10)
        self.origin = origin
        self.position = list(origin)
        self.radius = radius
        self.jerk=jerk
        self.velocity = [0,0]
        self.edgeHits = 0
        self.contained = contained
    def spotCoin(self,idx):
        radiusPortion = (self.position[idx]-self.origin[idx])/self.radius
        return 1 if os.urandom(1)[0]>=128+128*radiusPortion else -1
    def speedCoin(self,idx):
        if mag(self.velocity) == 0:
            return fairCoin()
        vmaxPortion = dist(self.velocity,(0,0))/self.vmax
        dimPortion = proj(scaleTo(vmaxPortion,self.velocity),(0,1) if idx else(1,0))
        return 1 if os.urandom(1)[0]>=128+128*dimPortion else -1
    def updateVelocity(self):
        self.velocity[0] += self.speedCoin(0)*self.jerk
        self.velocity[1] += self.speedCoin(1)*self.jerk
        self.velocity[0] += self.spotCoin(0)*self.jerk
        self.velocity[1] += self.spotCoin(1)*self.jerk
        if mag(self.velocity) > self.vmax:
            self.velocity[0] = int(self.velocity[0]*self.vmax/mag(self.velocity))
            self.velocity[1] = int(self.velocity[1]*self.vmax/mag(self.velocity))
    def nextPosition(self):
        self.updateVelocity()
        newPosition = [start+delta for start,delta in zip(self.position,self.velocity)]
        if dist(newPosition,self.origin) > self.radius:
            if self.contained:
                self.velocity = [0,0]
                self.edgeHits += 1
                print("Boundry Collisions: "+str(self.edgeHits)+"       ",end="\r")
        self.position = newPosition
        return self.position