🦋 Python’s Neon Butterfly Universe

 

Code:

import turtle import math import time screen = turtle.Screen() screen.setup(800, 800) screen.bgcolor("#02030a") t = turtle.Turtle() t.hideturtle() t.speed(0) t.width(2) colors = [ "#ff006e", "#ff7b00", "#ffe600", "#00ff9d", "#00e5ff", "#4169ff", "#9b30ff" ] # ----------------------------- # Butterfly Curve # ----------------------------- def butterfly(scale, color, phase): t.color(color) points = 260 for i in range(points): theta = i * 2 * math.pi / points # Butterfly curve r = math.exp(math.sin(theta)) - 2 * math.cos(4 * theta) x = scale * r * math.sin(theta + phase) y = scale * r * math.cos(theta + phase) if i == 0: t.penup() t.goto(x, y) t.pendown() else: t.goto(x, y) screen.update() time.sleep(0.004) # ----------------------------- # Outer butterfly # ----------------------------- for i in range(7): butterfly( 85 + i * 12, colors[i], i * 0.035 ) time.sleep(0.08) # ----------------------------- # Inner butterfly # ----------------------------- for i in range(5): butterfly( 35 + i * 8, colors[(i + 2) % len(colors)], -i * 0.04 ) time.sleep(0.08) # ----------------------------- # Body # ----------------------------- t.color("#ffffff") t.width(5) t.penup() t.goto(0, -115) t.pendown() t.goto(0, 115) screen.update() time.sleep(0.3) # ----------------------------- # Antennae # ----------------------------- t.width(2) for side in [-1, 1]: t.penup() t.goto(0, 110) t.setheading(90 + side * 35) t.pendown() for _ in range(35): t.forward(3) t.left(side * 2) screen.update() time.sleep(0.01) # ----------------------------- # Glowing body # ----------------------------- for r in range(18, 2, -3): t.penup() t.goto(0, -r) t.dot( r, colors[r % len(colors)] ) screen.update() time.sleep(0.05) # ----------------------------- # Star particles # ----------------------------- for i in range(45): angle = i * 137.5 radius = 180 + (i % 5) * 22 x = radius * math.cos(math.radians(angle)) y = radius * math.sin(math.radians(angle)) t.penup() t.goto(x, y) t.dot( 2 + i % 3, colors[i % len(colors)] ) screen.update() time.sleep(0.025) turtle.done()

Explanation:

1. Import Libraries

import turtle

import math

import time

turtle → Drawing.

math → Mathematical calculations.

time → Animation delays.

2. Create the Screen

screen = turtle.Screen()

screen.setup(800, 800)

screen.bgcolor("#02030a")

Creates the window.

Sets size to 800 × 800.

Adds a dark background.

3. Create the Turtle

t = turtle.Turtle()

t.hideturtle()

t.speed(0)

t.width(2)

Creates the drawing turtle.

Hides the cursor.

Sets maximum speed.

Sets line width to 2.

4. Define Colors

colors = [...]

Stores bright neon colors.

Colors are reused for the butterfly.

5. Define Butterfly Function

def butterfly(scale, color, phase):

Creates a reusable butterfly-drawing function.

scale → Size.

color → Line color.

phase → Rotation/offset.

6. Set Drawing Properties

t.color(color)

points = 260

Sets the selected color.

Uses 260 points for a smooth curve.

7. Calculate the Angle

theta = i * 2 * math.pi / points

Generates an angle for each point.

Covers a complete circular cycle.

8. Calculate Butterfly Radius

r = math.exp(math.sin(theta)) - 2 * math.cos(4 * theta)

Uses the butterfly-curve formula.

Produces the wing-like shape.

9. Calculate Coordinates

x = scale * r * math.sin(theta + phase)

y = scale * r * math.cos(theta + phase)

Calculates the X and Y positions.

scale controls the size.

phase slightly rotates the curve.

10. Draw the Curve

if i == 0:

    t.penup()

    t.goto(x, y)

    t.pendown()

else:

    t.goto(x, y)

Moves to the first point without drawing.

Connects all remaining points.

Creates the butterfly outline.

11. Animate the Curve

screen.update()

time.sleep(0.004)

Updates the screen.

Adds a tiny delay for animation.

12. Draw Outer Butterflies

for i in range(7):

Creates 7 outer butterfly layers.

butterfly(85 + i * 12, colors[i], i * 0.035)

Gradually increases the size.

Changes colors.

Adds a small phase shift.

13. Draw Inner Butterflies

for i in range(5):

Creates 5 smaller inner layers.

butterfly(

    35 + i * 8,

    colors[(i + 2) % len(colors)],

    -i * 0.04

)

Creates smaller curves.

Cycles through colors.

Applies reverse phase rotation.

14. Draw Butterfly Body

t.color("#ffffff")

t.width(5)

Changes the body to white.

Makes it thicker.

t.penup()

t.goto(0, -115)

t.pendown()

t.goto(0, 115)

Starts at the bottom.

Draws a vertical body through the center.

15. Draw Antennae

t.width(2)

for side in [-1, 1]:

Makes thinner lines.

Draws both antennae.

t.goto(0, 110)

t.setheading(90 + side * 35)

Moves to the top of the body.

Sets the antenna direction.

for _ in range(35):

Creates each antenna using 35 small segments.

t.forward(3)

t.left(side * 2)

Moves forward.

Slightly bends the antenna.

16. Create Glowing Body

for r in range(18, 2, -3):

Creates multiple shrinking circles.

t.dot(r, colors[r % len(colors)])

Draws colorful dots.

Creates a glowing effect.

17. Create Star Particles

for i in range(45):

Creates 45 particles around the butterfly.

angle = i * 137.5

radius = 180 + (i % 5) * 22

Generates different particle angles and distances.

Creates a scattered pattern.

18. Calculate Particle Position

x = radius * math.cos(math.radians(angle))

y = radius * math.sin(math.radians(angle))

Converts polar coordinates into X/Y positions.

19. Draw Particles

t.goto(x, y)

t.dot(

    2 + i % 3,

    colors[i % len(colors)]

)

Moves to each particle position.

Draws small colorful dots with varying sizes.

20. Finish

turtle.done()

Keeps the Turtle window open.

Ends the animation.