I’m working on creating a Fibonacci spiral with squares in R. I have successfully generated the Fibonacci sequence and plotted squares, but the alignment isn’t correct. The first square is not centered properly, causing issues with the spiral formation.

Here’s the R code I’ve used so far:

# Install ggplot2 if not already installed
install.packages("ggplot2")

# Load ggplot2
library(ggplot2)

# Define a function to generate Fibonacci numbers
fibonacci <- function(n) {
  fib_seq <- numeric(n)
  fib_seq[1] <- 1
  fib_seq[2] <- 1
  for (i in 3:n) {
    fib_seq[i] <- fib_seq[i-1] + fib_seq[i-2]
  }
  return(fib_seq)
}

# Generate the first 10 Fibonacci numbers
fib_seq <- fibonacci(10)

# Initialize the data frame
squares <- data.frame(x = numeric(10), y = numeric(10), size = fib_seq)

# Set the initial position
squares[1,] <- c(0, 0, fib_seq[1])
squares[2,] <- c(fib_seq[1], 0, fib_seq[2])

# Compute the coordinates for the rest of the squares
for (i in 3:10) {
  if (i %% 2 == 1) {
    # Odd index: Square goes above or below
    squares[i, "x"] <- squares[i-2, "x"]
    squares[i, "y"] <- squares[i-1, "y"] + squares[i-1, "size"]
  } else {
    # Even index: Square goes left or right
    squares[i, "x"] <- squares[i-1, "x"] + squares[i-1, "size"]
    squares[i, "y"] <- squares[i-2, "y"]
  }
}

# Plot the squares using ggplot2
ggplot(data = squares, aes(xmin = x, ymin = y, xmax = x + size, ymax = y + size)) +
  geom_rect(fill = "white", color = "black") + # Square boundaries
  coord_fixed(ratio = 1) + # Maintain aspect ratio
  theme_void() # Remove axis labels and grid lines

The problem is that the placement of the first two squares is not centered, causing misalignment with the Fibonacci spiral. I need the squares to be positioned such that:

• The first two squares are horizontally aligned.
• The subsequent squares are placed below, to the right, above, and to the left in the Fibonacci sequence order.

How can I correct the positioning of these squares to ensure that they align properly with the spiral?

This image is my target!