ulam_py2y41_v1

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# Filename: ulam_py2y41_v1.py
# Version: 1.0.1
# Author: Jeoi Reqi

"""
Ulam Spiral Visualizer Of Primes & Palindromic Primes On The Golden Line:

This Python script generates a spiral visualization of primes and palindromic primes.
The Ulam Spiral is a spiral arrangement of natural numbers, where the numbers are plotted on a grid & primes are highlighted.
In this script, the golden line is traced by the equation [P = y^2 - y + 41], where 'y' is the starting value determined by the user.
The golden line represents a diagonal line crossing the center where 'y' is.
Primes (indicated by red dots) & Palindromic Primes (indicated by blue dots) are distinctly marked, with some Primes being Palindromic Primes.

Requirements:
- Python 3
- Matplotlib

Usage:
- Run the script in a terminal or command prompt.
- Enter the starting value for 'y', which determines the plot's central starting point value.
- Enter the number of iterations of 'y' to be visualized in the spiral grid.
- The script will generate a plot and save it as a PNG file (e.g., 'y41_i100.png').
- The terminal output will be saved in a dynamically named text file (e.g., 'output_y41_i100.txt').

Note:
- The golden line is traced by the equation [P = y^2 - y + 41].
- Close the plot window to terminate the script.

Equation:   P=y^2-y+41

 Definition:
        Must be TRUE:
            [P] is a Prime
            [P] is possibly a Palindrome
            [y] is a natural whole integer
            [y] is a positive number
      !!    [y] is not less than 2  (y>2)
        (Note: P = Prime Pattern Breaks if y>2)


        Example: (if y = 4) Find P:

            [P = y^2-y+41]

            4^2-4+41 = P
            4x4-4+37 = P
            16-4 +37 = P
            12 + 37 = 49

            Prime Value is equal to (4 squared minus 4 plus 41)
            P = 49 (Prime)
"""

# Imports
import matplotlib.pyplot as plt
import time
import sys
import os

# Create an empty list to capture terminal output
terminal_output = []

plt.style.use('dark_background')
plt.ion()

# checks if a given number is prime or not
def is_prime(num):
    if num < 2:
        return False
    for i in range(2, int(num**0.5) + 1):
        if num % i == 0:
            return False
    return True

# change the x/y coordinates based on the state
def march(state, x, y):
    if state == 0:
        x += 1
    if state == 1:
        y += 1
    if state == 2:
        x -= 1
    if state == 3:
        y -= 1

    return x, y

# Create a list to capture the terminal output
terminal_output = []

# Ask the user for the starting number
y_value = int(input("Enter the starting number (y): "))

while y_value < 2:
    # If the user enters a starting number less than 2, prompt them to enter a valid one
    print("Please enter a starting number greater than or equal to 2.")
    y_value = int(input("Enter the starting number (y): "))

# Ask the user for the number of iterations
iterations_number = int(input("Enter the number of iterations (i): "))

# Initialize variables for the previous coordinates
l_x = 1
l_y = 0

# Initialize current coordinates based on user input
x = 0
y = y_value  # Use the user's input as the starting number

# Initialize variables for the Ulam Spiral algorithm
state = -1
factor = -1
steps = 1
current_steps = 0

# Record the start time for performance measurement
start_time = time.time()

# Create a list to store plot data
plot_data = []

# Create a dynamic filename for the plot
plot_filename = f"y{y_value}_i{iterations_number}.png"

# Create a single plot
fig, ax = plt.subplots()

# Loop through the range of iterations to generate points for the Ulam Spiral
for i in range(y_value, y_value + iterations_number):
    # Store the current coordinates as the previous coordinates
    l_x = x
    l_y = y

    # Increment the steps taken in the current direction
    current_steps += 1

    # Check if the current steps have reached the predefined number of steps
    if current_steps >= steps:
        # Increase the factor to change the direction of movement
        factor += 1
        current_steps = 0

        # Move to the next coordinates based on the Ulam Spiral algorithm
        x, y = march(state, x, y)

        # Increase the state to change the direction of movement
        state += 1

        # Reset the state to 0 if it exceeds 3 (four directions in total)
        if state > 3:
            state = 0

        # Change the factor after every two steps
        if factor == 2:
            factor = 0
            steps += 1

    # If the current steps are not 0, move to the next coordinates
    if current_steps != 0:
        x, y = march(state, x, y)

    # Define the two points to be plotted
    point1 = [x, y]
    point2 = [l_x, l_y]

    # Define the x and y values for plotting
    x_values = [point1[0], point2[0]]
    y_values = [point1[1], point2[1]]

    # Plot the line connecting the two points with a yellow color and reduced opacity
    ax.plot(x_values, y_values, 'y-', alpha=0.25)

    # Check if the current number in the iteration is a prime number
    if is_prime(i):
        # Check if the prime number is also a palindromic prime with at least two digits
        if str(i) == str(i)[::-1] and len(str(i)) >= 2:
            # Plot the point in blue if it is a palindromic prime
            ax.plot(x, y, 'bo')

            # Annotate the point with the palindromic prime number
            ax.annotate(i, (x, y), color='white', fontsize=8, ha='center', va='center')
        else:
            # Plot the point in red if it is a prime but not a palindromic prime
            ax.plot(x, y, 'ro')

    # Append the current iteration data to the plot_data list
    plot_data.append((i, x, y))


    # Set the dynamic title for the plot
    ax.set_title(f"y{y_value}_i{iterations_number}")

    # Remove ticks from the plot
    ax.set_xticks([])
    ax.set_yticks([])

    #plt.pause(0.001)  # Pause for a short duration to allow plotting if needed

    # Allow user early termination: Check if any figures are open, break the loop if not
    if not plt.get_fignums():
        print("Plotting terminated by user.")
        break

# Automatically save the image with a dynamic filename
plt.savefig(plot_filename)

# Close the figure to prevent issues with plt.show()
plt.close()

end_time = time.time()
elapsed_time = end_time - start_time

# Save the terminal output to a text file with a dynamic filename
output_filename = f"output_{plot_filename.replace('.png', '.txt')}"
with open(output_filename, "w") as file:
    # Write the starting value for 'y' and the number of iterations to the file
    file.write(f"value for y: {y_value}\n")
    file.write(f"Enter the number of iterations: {iterations_number}\n")
    file.write("\nResults:\n")

    # Iterate through the plot data to generate output for each iteration
    for data in plot_data:
        y_value, x_value, _ = data
        P = x_value**2 - x_value + y_value

        # Check if the calculated value (P) is a prime number
        if is_prime(P):
            # Check if the prime number is also a palindromic prime
            if is_prime(P) and str(P) == str(P)[::-1]:
                # Write the output for palindromic primes
                result_str = f"[y={y_value}, P={P}]   --   [PALINDROMIC PRIME]"
            else:
                # Write the output for non-palindromic primes
                result_str = f"[y={y_value}, P={P}]"

            # Write the result string to the file
            file.write(result_str + "\n")

# Terminal Output Messages
print(f"\nPlot data saved to 'plot_data.txt'\n")
print(f"\nTerminal output saved to {output_filename}\n")

# Print the elapsed time in hours, minutes, and seconds format
hours, remainder = divmod(elapsed_time, 3600)
minutes, seconds = divmod(remainder, 60)
print(f"\nTime elapsed: {int(hours)} hours, {int(minutes)} minutes, {seconds:.2f} seconds\n")