Hello everyone welcome to this projects on the implementation of the Phyllotaxis

Before We start I strongly suggest you to watch this video for some explanation phyllotaxis (youtube auctux).

In botany, phyllotaxis or phyllotaxy is the arrangement of leaves on a plant stem (from Ancient Greekphýllon "leaf" and táxis "arrangement").[1] Phyllotactic spirals form a distinctive class of patterns in nature.

For this project we gonna be using pygame, if you don't have pygame you can install it just by running this command in your terminal "pip install pygame".

We gonna start by importing the libraries that we gonna use and initialize our pygame and some constant variables like the width and the height of the screen.

import pygame
import os
import colorsys
from math import sqrt, cos, sin

os.environ["SDL_VIDEO_CENTERED"]='1'

width, height = 1920, 1080
size = (width, height)
pygame.init()
pygame.display.set_caption("Phyllotaxis")
screen = pygame.display.set_mode(size)
fps = 30
clock = pygame.time.Clock()

font = pygame.font.Font('freesansbold.ttf', 14)

rotation_angle = 0
white, black = (240, 240, 240), (15, 15, 15)
hue = 0

Let declare some variables and make a Point class that gonna store position and color , and make a function to convert hsv color to rgb.

we also gonna create an array that gonna store our points

n = 0
c = 20
cube_position = [width//2, height//2]
scale = 20
points = []
counter = False
class Point:
    def __init__(self, x, y, color):
        self.x = x
        self.y = y
        self.points= [[x], [y], [1]]
        self.color = color

def hsv2rgb(h, s, v):
    return tuple(round(i * 255) for i in colorsys.hsv_to_rgb(h, s, v))

let add a matrix multiplication function and some rotation matrices , this is not necessary . I added it so that we can be able to rotate our point in 3Dimension easily since pygame doesn't support 3D.

we will initialize too our main loop for our simulation.

def matrix_multiplication(a, b):
    columns_a = len(a[0])
    rows_a = len(a)
    columns_b = len(b[0])
    rows_b = len(b)

    result_matrix = [[j for j in range(columns_b)] for i in range(rows_a)]
    if columns_a == rows_b:
        for x in range(rows_a):
            for y in range(columns_b):
                sum = 0
                for k in range(columns_a):
                    sum += a[x][k] * b[k][y]
                result_matrix[x][y] = sum
        return result_matrix
    else:
        print("error! the columns of the first matrix must be equal with the rows of the second matrix")
        return None

run = True
while run:
    clock.tick(fps)
    screen.fill(black)
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False

    angle = n * 137.5
    r = c * sqrt(n)

    x = r * cos(angle)
    y = r * sin(angle)

    rotation_z =[[cos(rotation_angle), -sin(rotation_angle), 0],
                     [sin(rotation_angle), cos(rotation_angle), 0 ],
                      [0, 0, 1]]

and At last let put it together:

run = True
while run:
    clock.tick(fps)
    screen.fill(black)
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False

    angle = n * 137.5
    r = c * sqrt(n)

    x = r * cos(angle)
    y = r * sin(angle)

    rotation_z =[[cos(rotation_angle), -sin(rotation_angle), 0],
                     [sin(rotation_angle), cos(rotation_angle), 0 ],
                      [0, 0, 1]]
    if n < 700:
        # coloring type hsv2rgb(hue, 1, 1) for a rainbow pattern
        # hsv2rgb(angle/255, 1, 1) for a spiral rainbow pattern
        p = Point(int(x), int(y), hsv2rgb(angle/255, 1, 1))
        points.append(p)

    for point in points:
        rotated_2d = matrix_multiplication(rotation_z, point.points)

        distance = 20
        z = 1/(distance - rotated_2d[2][0])
        projection_matrix = [[z, 0, 0],
                             [0, z, 0]]
        projected2d = matrix_multiplication(projection_matrix, rotated_2d)
        x_pos = int(projected2d[0][0] * scale) + cube_position[0]
        y_pos = int(projected2d[1][0] * scale) + cube_position[1]
        pygame.draw.circle(screen, point.color, (x_pos, y_pos), 8)

    text = font.render(str(int(r)), True, white)
    textRect = text.get_rect()
    textRect.center = (50, 100)
    screen.blit(text, textRect)
    pygame.display.update()

    n += 1
    hue += 0.003
    rotation_angle += 0.01
pygame.quit()

Youtube channel: Auctux

Github link: Phyllotaxis Github

thank you ✌️