{"id":158,"date":"2025-03-27T15:40:00","date_gmt":"2025-03-27T15:40:00","guid":{"rendered":"https:\/\/theroyalscode.com\/students\/a_carpenter\/?p=158"},"modified":"2025-03-27T15:42:34","modified_gmt":"2025-03-27T15:42:34","slug":"free-thursday-3-27-2025","status":"publish","type":"post","link":"https:\/\/theroyalscode.com\/students\/a_carpenter\/2025\/03\/27\/free-thursday-3-27-2025\/","title":{"rendered":"Free Thursday 3\/27\/2025"},"content":{"rendered":"\n

Today I did testing with something I’ve been working on over this past week. I have been working with Python Turtle Graphics and have been trying to make the Sierpisnki triangle with rainbow colors and I finally, finally, finally have found the proper algorithm, so here it is, the code for it alongside an image of the successful small-scale test<\/strong><\/p>\n\n\n\n

from turtle import *\nimport time\n\n# Set the color mode to RGB\ncolormode(255)\n\n# Set the background color to black\nbgcolor(0, 0, 0)\n\n# Function to generate rainbow colors\ndef rainbow_color_interpolation(num_colors):\n    colors = []\n    for i in range(num_colors):\n        # Calculate the hue value\n        hue = i \/ num_colors * 360\n        # Convert HSV to RGB\n        rgb = hsv_to_rgb(hue \/ 360.0, 1.0, 1.0)\n        colors.append((int(rgb[0] * 255), int(rgb[1] * 255), int(rgb[2] * 255)))\n    return colors\n\ndef hsv_to_rgb(h, s, v):\n    if s == 0.0:  # Achromatic (grey)\n        return (v, v, v)\n    i = int(h * 6.0)  # Assume h is [0, 1)\n    f = (h * 6.0) - i\n    p = v * (1.0 - s)\n    q = v * (1.0 - f * s)\n    t = v * (1.0 - (1.0 - f) * s)\n    i = i % 6\n    if i == 0:\n        return (v, t, p)\n    elif i == 1:\n        return (q, v, p)\n    elif i == 2:\n        return (p, v, t)\n    elif i == 3:\n        return (p, q, v)\n    elif i == 4:\n        return (t, p, v)\n    elif i == 5:\n        return (v, p, q)\n\n# Setup turtle\nspeed(0)\nwidth(1)\ncount = 0 \n\ndef draw_triangle(length):\n    global count\n    # Use interpolated colors for the triangle\n    color(rainbow_colors[count % len(rainbow_colors)])\n    count += 1\n    forward(length)\n    right(120)\n    color(rainbow_colors[count % len(rainbow_colors)])\n    count += 1\n    forward(length)\n    right(120)\n\ndef draw_sierpinski(length):\n    draw_triangle(length)\n    if length > 10:\n        draw_sierpinski(length \/\/ 2)\n    draw_triangle(length)\n    if length > 10:\n        draw_sierpinski(length \/\/ 2)\n    draw_triangle(length)\n    if length > 10:\n        draw_sierpinski(length \/\/ 2)\n    draw_triangle(length)\n    if length > 10:\n        draw_sierpinski(length \/\/ 2)\n    draw_triangle(length)\n    if length >= 10:\n        draw_sierpinski(length \/\/ 2)\n    draw_triangle(length)\n\n\n\n\n\n\n# Generate rainbow colors\nnum_colors = 6 # You can adjust this number for more or fewer colors\nrainbow_colors = rainbow_color_interpolation(num_colors)\n\n# Main drawing loop\nwhile True:\n    for color_value in rainbow_colors:\n        color(color_value)  # Set the turtle color\n        draw_sierpinski(120)\n        # Pause for a moment before the next drawing<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
And an image from Pennwest\/Edinboro’s Chaos Game Website (This Website is super cool check it out at prodweb2.cis.pennwest.edu\/sierpinski\/<\/a><\/strong>): <\/strong><\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
As can be seen, the program successfully makes a Sierpinski’s Triangle despite taking a very long time even for just this small one, I have tried to tweak the numbers to fix this issue, but I haven’t yet found any values that would make it work properly and make a true Sierpinski triangle as I have found can be made. I will now show a larger scale test with a length increase of 100:<\/strong><\/p>\n\n\n\n