Two Dimensional Random Walks

[spsanderson]

Some 2D random walks:

# Load required libraries
library(ggplot2)
library(dplyr)

# Function to generate a 2D random walk
generate_random_walk <- function(n_steps = 100) {
  # Generate random steps
  x_steps <- sample(c(-1, 1), n_steps, replace = TRUE)
  y_steps <- sample(c(-1, 1), n_steps, replace = TRUE)
  
  # Calculate positions
  x_positions <- cumsum(x_steps)
  y_positions <- cumsum(y_steps)
  
  # Create a data frame
  walk_df <- data.frame(
    Step = 1:n_steps,
    X = x_positions,
    Y = y_positions
  )
  
  return(walk_df)
}

# Generate a random walk
random_walk_df <- generate_random_walk(n_steps = 1000)

# Plot the random walk
ggplot(random_walk_df, aes(x = X, y = Y)) +
  geom_path(color = "blue", alpha = 0.7) +
  geom_point(color = "red", size = 1) +
  theme_minimal() +
  labs(
    title = "2D Random Walk",
    x = "X Position",
    y = "Y Position"
  ) +
  theme(axis.text.x=element_blank(), #remove x axis labels
        axis.ticks.x=element_blank(), #remove x axis ticks
        axis.text.y=element_blank(),  #remove y axis labels
        axis.ticks.y=element_blank()  #remove y axis ticks
  )

# Function to simulate a 2D random walk
random_walk <- function(steps = 1000, step_size = 1) {
  x <- cumsum(runif(steps, -step_size, step_size))
  y <- cumsum(runif(steps, -step_size, step_size))
  data.frame(step = 1:steps, x = x, y = y)
}

# Generate random walk data
walk_data <- random_walk(steps = 1000, step_size = 0.5)

# Plot the random walk
ggplot(walk_data, aes(x = x, y = y)) +
  geom_path(aes(color = step), linewidth = 0.5) +
  geom_point(data = walk_data[c(1, max(walk_data[["step"]])), ], 
             aes(color = step), size = 3) +
  scale_color_viridis_c(option = "turbo") +
  labs(title = "2D Random Walk",
       x = "X Position",
       y = "Y Position") +
  theme_minimal() +
  theme(legend.position = "none") +
  theme(axis.text.x=element_blank(), #remove x axis labels
        axis.ticks.x=element_blank(), #remove x axis ticks
        axis.text.y=element_blank(),  #remove y axis labels
        axis.ticks.y=element_blank()  #remove y axis ticks
  )

# Set random seed for reproducibility
set.seed(123)

# Number of steps
n <- 1000

# Generate random walk
random_walk <- data.frame(
  x = cumsum(rnorm(n)),
  y = cumsum(rnorm(n)),
  step = 1:n
)

# Create the plot
ggplot(random_walk, aes(x = x, y = y)) +
  geom_path(aes(color = step), linewidth = 0.5) +
  geom_point(data = random_walk[c(1, n), ], aes(color = step), size = 3) +
  scale_color_viridis_c(option = "plasma") +
  labs(title = "2D Random Walk",
       x = "X Position",
       y = "Y Position") +
  theme_minimal() +
  theme(legend.position = "none") +
  theme(axis.text.x=element_blank(), #remove x axis labels
        axis.ticks.x=element_blank(), #remove x axis ticks
        axis.text.y=element_blank(),  #remove y axis labels
        axis.ticks.y=element_blank()  #remove y axis ticks
  )