Draw Fractal Image By Python

A Python fractal drawing library supporting Julia Set, Mandelbrot Set, IFS, L-System and more.

Install

pip install fractal

Or download the package:

pip install -e .

Dependencies:

• Pillow >= 8.0.0
• numpy >= 1.20.0

Features

• Julia Set - Interactive zoom with mouse
• Mandelbrot Set - Classic Mandelbrot fractal
• IFS - Iterated Function System (fern, leaf, tree, etc.)
• L-System - Lindenmayer System (Koch curve, dragon, tree, etc.)
• CIFS - Complex Iterated Function System

GUI Operations

• Save: Click "Save" button or Ctrl+P
• Save As: Click "Save As..." to choose format (PNG/JPG/BMP)
• Zoom In: Left click to show selection box, drag to move, click again to confirm
• Zoom Out: Right click
• Cancel Selection: Press ESC or right click

Examples

L-System

from fractal import Pen
from math import sqrt
p = Pen([350, 270])
p.setPoint([140, 60])
p.setWidth(1)
p.doD0L(omega="L", P={"L": "L+R", "R": "L-R"},
              delta=90, times=15, length=200, rate=sqrt(2))
p.wait()

from fractal import Pen

p = Pen([500, 500], title="Window")
p.setPoint([495, 495])
p.setAngle(90)
p.doD0L(omega="f+f+f+f", P={"f": "ff+f--f+f"},
        delta=90, times=5, length=490, rate=3)
p.wait()

from fractal import Pen
p = Pen([420,420])
p.setPoint([10,10])
p.doD0L(omega = "L", P = {"L": "LFRFL-FF-RFLFR+FF+LFRFL", "R": "RFLFR+FF+LFRFL-FF-RFLFR"}, delta =  90, times = 4, length = 200 , rate = 3)
p.wait()

from fractal import Pen
p = Pen([400, 470])
p.setAngle(90)
p.setPoint([200,470])
p.doD0L(omega = "f", P = {"f": "h[-f][+f]hf", "h": "hh"}, delta = 25.7, times = 7, length = 400, rate = 2.17)
p.wait()

from fractal import Pen
p = Pen([400, 470])
p.setAngle(90)
p.setPoint([170, 470])
p.doD0L(omega="f", P={"f": "h+[[f]-f]-h[-hf]+f", "h": "hh"},
        delta=22.5, times=6, length=400, rate=2.3)
p.wait()

IFS

from fractal import IFS
from random import random

def ifsp(x, y):
    p = random()
    if p < 0.01:
        return (0, 0.16 * y)
    elif p < 0.07:
        if random() > 0.5:
            return (0.21 * x - 0.25 * y, 0.25 * x + 0.21 * y + 0.44)
        else:
            return (-0.2 * x + 0.26 * y, 0.23 * x + 0.22 * y + 0.6)
    else:
        return (0.85 * x + 0.1 * y, -0.05 * x + 0.85 * y + 0.6)

ob = IFS([400, 500], title = "Leaf")
ob.setPx(100, 100, 100)
ob.setIfsp(ifsp)
ob.doIFS(200000)
ob.wait()

# Box IFS
from fractal import IFS
from random import randint


def ifsp(x, y):
    p = randint(1, 5)
    if p == 1:
        return (x / 3, y / 3)
    elif p == 2:
        return (x / 3 + 2 / 3, y / 3)
    elif p == 3:
        return (x / 3 + 1 / 3, y / 3 + 1 / 3)
    elif p == 4:
        return (x / 3, y / 3 + 2 / 3)
    else:
        return (x / 3 + 2 / 3, y / 3 + 2 / 3)

ob = IFS([500, 500], title="Box")
ob.setPx(490, 5, 5)
ob.setIfsp(ifsp)
ob.doIFS(200000)
ob.wait()

from fractal import IFS

ifscode = [
    [0.879, 0.054, -0.051, 0.878, 0.077, 0.123, 0.123],
    [0.1, -0.193, 0.285, 0.224, 0.174, 0.169, 0.169],
    [0.008, 0.135, 0, 0.204, 0.075, 0.074, 0.074],
    [0.402, 0.045, 0.016, -0.197, 0.111, 0.193, 0.193]
]

ifs = IFS([500, 500])
ifs.setPx(700, 0, 0)
ifs.setIfsCode(ifscode)
ifs.doIFS(200000)
ifs.wait()

from fractal import IFS

code = [
    [0.195, -0.488, 0.344, 0.443, 0.4431, 0.2452, 0.2],
    [0.462, 0.414, -0.252, 0.361, 0.2511, 0.5692, 0.2],
    [-0.637, 0, 0, 0.501, 0.8562, 0.2512, 0.2],
    [-0.035, 0.07, -0.469, 0.022, 0.4884, 0.5069, 0.2],
    [-0.058, -0.07, -0.453, -0.111, 0.5976, 0.0969, 0.2]
]

ifs = IFS([500,500])
ifs.setCoordinate()
ifs.setPx(500, 0, 0)
ifs.setIfsCode(code)
ifs.doIFS(200000)
ifs.wait()

Julia

from fractal import Julia
ju = Julia([500, 500])
ju.setC(0 - 1j)
ju.doJulia(500)
ju.wait()

-1.25 + 0j

-0.605-0.45j

Mandelbrot

from fractal import Mandelbrot
man = Mandelbrot([500, 500])
man.setRange(5, 5)
man.doMandelbrot(200)
man.wait()

License

MIT License

Author

L.Chen (pysrc)