पायथन में फ्रैक्टल्स। पूर्वाभ्यास

भग्न एक ऐसी वस्तु या मात्रा है जो किसी भी पैमाने पर आत्म-समानता (औपचारिक अर्थों में) को प्रदर्शित करती है। एक वस्तु अलग-अलग पैमानों पर समान संरचनाओं को नहीं दिखाती है, लेकिन समान "प्रकार" की संरचनाएं भग्न के सभी स्तरों पर दिखाई देती हैं। इस मामले में, ग्राफ़ को एक लॉगरिदमिक स्केल के साथ एक समन्वय प्रणाली में प्लॉट किया जाता है, जहां परिमाण और पैमाने को अक्षों के साथ गिना जाता है, ग्राफ़ एक सीधी रेखा है जिसमें ढलान के साथ फ्रैक्टल के आयाम को दर्शाया गया है। - मैथ वर्ल्ड

• क्रॉल आगे
• बाएं कोण को घुमाएं
• दाहिने कोण को घुमाएं

• मूक रिकॉर्ड
• रिकॉर्डिंग सक्षम करें

लिंडेनमेयर प्रणाली, जिसे एल-प्रणाली के रूप में भी जाना जाता है, एक पंक्ति पुनर्लेखन तंत्र है जिसका उपयोग 1 से 2 तक आयामों के साथ भग्न उत्पन्न करने के लिए किया जा सकता है - गणित विश्व

• : , L-.
• : .
• : , .

• F: आगे क्रॉल करें
• +: दाएँ मुड़ें
• -: बांए मुड़िए

axiom = "F--F--F"
rules = {"F":"F+F--F+F"}
iterations = 4 # TOP: 7
angle = 60

axiom = "F+F+F+F"
rules = {"F":"F-F+F+FFF-F-F+F"}
iterations = 2 # TOP: 4
angle = 90

axiom = "F+F+F+F"
rules = {"F":"FF+F++F+F"}
iterations = 3 # TOP: 6
angle = 90

axiom = "F--F"
rules = {"F":"F-F+F+F-F"}
iterations = 4 # TOP: 6
angle = 90

axiom = "F-F-F-F"
rules = {"F":"F-F+F+F-F"}
iterations = 4 # TOP: 6
angle = 90

axiom = "F"
rules = {"F":"+F--F+"}
iterations = 10 # TOP: 16
angle = 45

axiom = "YF"
rules = {"X":"YF+XF+Y", "Y":"XF-YF-X"}
iterations = 1 # TOP: 10
angle = 60

axiom = "FXF--FF--FF"
rules = {"F":"FF", "X":"--FXF++FXF++FXF--"}
iterations = 7 # TOP: 8
angle = 60

axiom = "F+F+F+F"
rules = {"F":"FF+F+F+F+FF"}
iterations = 3 # TOP: 5
angle = 90

axiom = "F+F+F+F"
rules = {"F":"FF+F-F+F+FF"}
iterations = 3 # TOP: 4
angle = 90

axiom = "F+F+F+F"
rules = {"F":"FF+F+F+F+F+F-F"}
iterations = 2 # TOP: 4
angle = 90

axiom = "F+F+F+F"
rules = {"F":"F+F-F+F+F"}
iterations = 3 # TOP: 6
angle = 90

axiom = "F++F++F++F++F"
rules = {"F":"F++F++F+++++F-F++F"}
iterations = 1 # TOP: 5
angle = 36

axiom = "F+F+F+F"
rules = {"F":"-F+F-F-F+F+FF-F+F+FF+F-F-FF+FF-FF+F+F-FF-F-F+FF-F-F+F+F-F+"}
iterations = 3 # TOP: 3
angle = 90

axiom = "FX"
rules = {"X":"X+YF++YF-FX--FXFX-YF+", "Y":"-FX+YFYF++YF+FX--FX-Y"}
iterations = 4 # TOP: 6
angle = 60

axiom = "F+XF+F+XF"
rules = {"X":"XF-F+F-XF+F+XF-F+F-X"}
iterations = 4 # TOP: 8
angle = 90

axiom = " -X--X"
rules = {"X":"XFX--XFX"}
iterations = 3 # TOP: 9
angle = 45

axiom = "YF"
rules = {"X": "XFX-YF-YF+FX+FX-YF-YFFX+YF+FXFXYF-FX+YF+FXFX+YF-FXYF-YF-FX+FX+YFYF-", 
        "Y": "+FXFX-YF-YF+FX+FXYF+FX-YFYF-FX-YF+FXYFYF-FX-YFFX+FX+YF-YF-FX+FX+YFY"}
iterations = 2 # TOP: 3
angle = 90

axiom = "LFL-F-LFL"
rules = {"L":"+RF-LFL-FR+", "R":"-LF+RFR+FL-"}
iterations = 0 # TOP: 8
angle = 90

axiom = "L"
rules = {"L":"+RF-LFL-FR+", "R":"-LF+RFR+FL-"}
iterations = 8 # TOP: 9
angle = 90

axiom = "X"
rules = {"X":"XFYFX+F+YFXFY-F-XFYFX", "Y":"YFXFY-F-XFYFX+F+YFXFY"}
iterations = 4 # TOP: 6
angle = 90

axiom = "F"
rules = {"F":"F+F-F-F-F+F+F+F-F"}
iterations = 2 # TOP: 5
angle = 90

axiom = "F+F+F+F"
rules = {"F":"F+FF++F+F"}
iterations = 3 # TOP: 6
angle = 90

axiom = "F+F+F"
rules = {"F":"F-F+F"}
iterations = 2 # TOP: 9
angle = 120

axiom = "FX"
rules = {"X":"X+YF+", "Y":"-FX-Y"}
iterations = 8 # TOP: 16
angle = 90

axiom = "F"
rules = {"F":"F-F+F"}
iterations = 5 # TOP: 10
angle = 120

axiom = "FX+FX"
rules = {"X":"X+YF+", "Y":"-FX-Y"}
iterations = 6 # TOP: 16
angle = 90

axiom = "FX+FX+FX"
rules = {"X":"X+YF+", "Y":"-FX-Y"}
iterations = 7 # TOP: 15
angle = 90

import turtle

def create_l_system(iters, axiom, rules):
    start_string = axiom
    if iters == 0:
        return axiom
    end_string = ""
    for _ in range(iters):
        end_string = "".join(rules[i] if i in rules else i for i in start_string)
        start_string = end_string

    return end_string


def draw_l_system(t, instructions, angle, distance):
    for cmd in instructions:
        if cmd == 'F':
            t.forward(distance)
        elif cmd == '+':
            t.right(angle)
        elif cmd == '-':
            t.left(angle)


def main(iterations, axiom, rules, angle, length=8, size=2, y_offset=0,
        x_offset=0, offset_angle=0, width=450, height=450):

    inst = create_l_system(iterations, axiom, rules)

    t = turtle.Turtle()
    wn = turtle.Screen()
    wn.setup(width, height)

    t.up()
    t.backward(-x_offset)
    t.left(90)
    t.backward(-y_offset)
    t.left(offset_angle)
    t.down()
    t.speed(0)
    t.pensize(size)
    draw_l_system(t, inst, angle, length)
    t.hideturtle()

    wn.exitonclick()

import turtle

def create_l_system(iters, axiom, rules):
    start_string = axiom
    if iters == 0:
        return axiom
    end_string = ""
    for _ in range(iters):
        end_string = "".join(rules[i] if i in rules else i for i in start_string)
        start_string = end_string

    return end_string

def draw_l_system(t, instructions, angle, distance):
    for cmd in instructions:
        if cmd == 'F':
            t.forward(distance)
        elif cmd == '+':
            t.right(angle)
        elif cmd == '-':
            t.left(angle)

def main(iterations, axiom, rules, angle, length=8, size=2, y_offset=0,
        x_offset=0, offset_angle=0, width=450, height=450):

    inst = create_l_system(iterations, axiom, rules)

    t = turtle.Turtle()
    wn = turtle.Screen()
    wn.setup(width, height)

    t.up()
    t.backward(-x_offset)
    t.left(90)
    t.backward(-y_offset)
    t.left(offset_angle)
    t.down()
    t.speed(0)
    t.pensize(size)
    draw_l_system(t, inst, angle, length)
    t.hideturtle()

    wn.exitonclick()