defmandelbrot(width:int,height:int,*,

x:float=-0.5,y:float=0,zoom:int=1,max_iterations:int=100)->np.array:

x_width,y_height=1.5,1.5*height/width

x_from,x_to=x-x_width/zoom,x+x_width/zoom

y_from,y_to=y-y_height/zoom,y+y_height/zoom

x=np.linspace(x_from,x_to,width).reshape((1,width))

y=np.linspace(y_from,y_to,height).reshape((height,1))

z=np.zeros(c.shape,dtype=np.complex128)

div_time=np.zeros(z.shape,dtype=int)

m=np.full(c.shape,True,dtype=bool)

foriinrange(max_iterations):

z[m]=z[m]**2+c[m]

diverged=np.greater(np.abs(z),2,out=np.full(c.shape,False),where=m)# Find diverging

div_time[diverged]=i# set the value of the diverged iteration number

m[np.abs(z)>2]=False# to remember which have diverged

defjulia(width:int,height:int,*,

c:complex=-0.4+0.6j,x:float=0,y:float=0,zoom:int=1,max_iterations:int=100)->np.array:

x_width,y_height=1.5,1.5*height/width

x_from,x_to=x-x_width/zoom,x+x_width/zoom

y_from,y_to=y-y_height/zoom,y+y_height/zoom

x=np.linspace(x_from,x_to,width).reshape((1,width))

y=np.linspace(y_from,y_to,height).reshape((height,1))

c=np.full(z.shape,c)

div_time=np.zeros(z.shape,dtype=int)

m=np.full(c.shape,True,dtype=bool)

foriinrange(max_iterations):

z[m]=z[m]**2+c[m]

m[np.abs(z)>2]=False

div_time[m]=i

- numpy

- paths:

- /palettes.py

- /fractals.py

from pyodide import to_js

import numpy as np

from palettes import Magma256

from fractals import mandelbrot, julia

from js import (

console,

document,

CanvasRenderingContext2D as Context2d,

)

Magma256 = np.array([

[0x00, 0x00, 0x03], [0x00, 0x00, 0x04], [0x00, 0x00, 0x06], [0x01, 0x00, 0x07], [0x01, 0x01, 0x09], [0x01, 0x01, 0x0b],

[0x02, 0x02, 0x0d], [0x02, 0x02, 0x0f], [0x03, 0x03, 0x11], [0x04, 0x03, 0x13], [0x04, 0x04, 0x15], [0x05, 0x04, 0x17],

[0x06, 0x05, 0x19], [0x07, 0x05, 0x1b], [0x08, 0x06, 0x1d], [0x09, 0x07, 0x1f], [0x0a, 0x07, 0x22], [0x0b, 0x08, 0x24],

[0x0c, 0x09, 0x26], [0x0d, 0x0a, 0x28], [0x0e, 0x0a, 0x2a], [0x0f, 0x0b, 0x2c], [0x10, 0x0c, 0x2f], [0x11, 0x0c, 0x31],

[0x12, 0x0d, 0x33], [0x14, 0x0d, 0x35], [0x15, 0x0e, 0x38], [0x16, 0x0e, 0x3a], [0x17, 0x0f, 0x3c], [0x18, 0x0f, 0x3f],

[0x1a, 0x10, 0x41], [0x1b, 0x10, 0x44], [0x1c, 0x10, 0x46], [0x1e, 0x10, 0x49], [0x1f, 0x11, 0x4b], [0x20, 0x11, 0x4d],

[0x22, 0x11, 0x50], [0x23, 0x11, 0x52], [0x25, 0x11, 0x55], [0x26, 0x11, 0x57], [0x28, 0x11, 0x59], [0x2a, 0x11, 0x5c],

[0x2b, 0x11, 0x5e], [0x2d, 0x10, 0x60], [0x2f, 0x10, 0x62], [0x30, 0x10, 0x65], [0x32, 0x10, 0x67], [0x34, 0x10, 0x68],

[0x35, 0x0f, 0x6a], [0x37, 0x0f, 0x6c], [0x39, 0x0f, 0x6e], [0x3b, 0x0f, 0x6f], [0x3c, 0x0f, 0x71], [0x3e, 0x0f, 0x72],

[0x40, 0x0f, 0x73], [0x42, 0x0f, 0x74], [0x43, 0x0f, 0x75], [0x45, 0x0f, 0x76], [0x47, 0x0f, 0x77], [0x48, 0x10, 0x78],

[0x4a, 0x10, 0x79], [0x4b, 0x10, 0x79], [0x4d, 0x11, 0x7a], [0x4f, 0x11, 0x7b], [0x50, 0x12, 0x7b], [0x52, 0x12, 0x7c],

[0x53, 0x13, 0x7c], [0x55, 0x13, 0x7d], [0x57, 0x14, 0x7d], [0x58, 0x15, 0x7e], [0x5a, 0x15, 0x7e], [0x5b, 0x16, 0x7e],

[0x5d, 0x17, 0x7e], [0x5e, 0x17, 0x7f], [0x60, 0x18, 0x7f], [0x61, 0x18, 0x7f], [0x63, 0x19, 0x7f], [0x65, 0x1a, 0x80],

[0x66, 0x1a, 0x80], [0x68, 0x1b, 0x80], [0x69, 0x1c, 0x80], [0x6b, 0x1c, 0x80], [0x6c, 0x1d, 0x80], [0x6e, 0x1e, 0x81],

[0x6f, 0x1e, 0x81], [0x71, 0x1f, 0x81], [0x73, 0x1f, 0x81], [0x74, 0x20, 0x81], [0x76, 0x21, 0x81], [0x77, 0x21, 0x81],

[0x79, 0x22, 0x81], [0x7a, 0x22, 0x81], [0x7c, 0x23, 0x81], [0x7e, 0x24, 0x81], [0x7f, 0x24, 0x81], [0x81, 0x25, 0x81],

[0x82, 0x25, 0x81], [0x84, 0x26, 0x81], [0x85, 0x26, 0x81], [0x87, 0x27, 0x81], [0x89, 0x28, 0x81], [0x8a, 0x28, 0x81],

[0x8c, 0x29, 0x80], [0x8d, 0x29, 0x80], [0x8f, 0x2a, 0x80], [0x91, 0x2a, 0x80], [0x92, 0x2b, 0x80], [0x94, 0x2b, 0x80],

[0x95, 0x2c, 0x80], [0x97, 0x2c, 0x7f], [0x99, 0x2d, 0x7f], [0x9a, 0x2d, 0x7f], [0x9c, 0x2e, 0x7f], [0x9e, 0x2e, 0x7e],

[0x9f, 0x2f, 0x7e], [0xa1, 0x2f, 0x7e], [0xa3, 0x30, 0x7e], [0xa4, 0x30, 0x7d], [0xa6, 0x31, 0x7d], [0xa7, 0x31, 0x7d],

[0xa9, 0x32, 0x7c], [0xab, 0x33, 0x7c], [0xac, 0x33, 0x7b], [0xae, 0x34, 0x7b], [0xb0, 0x34, 0x7b], [0xb1, 0x35, 0x7a],

[0xb3, 0x35, 0x7a], [0xb5, 0x36, 0x79], [0xb6, 0x36, 0x79], [0xb8, 0x37, 0x78], [0xb9, 0x37, 0x78], [0xbb, 0x38, 0x77],

[0xbd, 0x39, 0x77], [0xbe, 0x39, 0x76], [0xc0, 0x3a, 0x75], [0xc2, 0x3a, 0x75], [0xc3, 0x3b, 0x74], [0xc5, 0x3c, 0x74],

[0xc6, 0x3c, 0x73], [0xc8, 0x3d, 0x72], [0xca, 0x3e, 0x72], [0xcb, 0x3e, 0x71], [0xcd, 0x3f, 0x70], [0xce, 0x40, 0x70],

[0xd0, 0x41, 0x6f], [0xd1, 0x42, 0x6e], [0xd3, 0x42, 0x6d], [0xd4, 0x43, 0x6d], [0xd6, 0x44, 0x6c], [0xd7, 0x45, 0x6b],

[0xd9, 0x46, 0x6a], [0xda, 0x47, 0x69], [0xdc, 0x48, 0x69], [0xdd, 0x49, 0x68], [0xde, 0x4a, 0x67], [0xe0, 0x4b, 0x66],

[0xe1, 0x4c, 0x66], [0xe2, 0x4d, 0x65], [0xe4, 0x4e, 0x64], [0xe5, 0x50, 0x63], [0xe6, 0x51, 0x62], [0xe7, 0x52, 0x62],

[0xe8, 0x54, 0x61], [0xea, 0x55, 0x60], [0xeb, 0x56, 0x60], [0xec, 0x58, 0x5f], [0xed, 0x59, 0x5f], [0xee, 0x5b, 0x5e],

[0xee, 0x5d, 0x5d], [0xef, 0x5e, 0x5d], [0xf0, 0x60, 0x5d], [0xf1, 0x61, 0x5c], [0xf2, 0x63, 0x5c], [0xf3, 0x65, 0x5c],

[0xf3, 0x67, 0x5b], [0xf4, 0x68, 0x5b], [0xf5, 0x6a, 0x5b], [0xf5, 0x6c, 0x5b], [0xf6, 0x6e, 0x5b], [0xf6, 0x70, 0x5b],

[0xf7, 0x71, 0x5b], [0xf7, 0x73, 0x5c], [0xf8, 0x75, 0x5c], [0xf8, 0x77, 0x5c], [0xf9, 0x79, 0x5c], [0xf9, 0x7b, 0x5d],

[0xf9, 0x7d, 0x5d], [0xfa, 0x7f, 0x5e], [0xfa, 0x80, 0x5e], [0xfa, 0x82, 0x5f], [0xfb, 0x84, 0x60], [0xfb, 0x86, 0x60],

[0xfb, 0x88, 0x61], [0xfb, 0x8a, 0x62], [0xfc, 0x8c, 0x63], [0xfc, 0x8e, 0x63], [0xfc, 0x90, 0x64], [0xfc, 0x92, 0x65],

[0xfc, 0x93, 0x66], [0xfd, 0x95, 0x67], [0xfd, 0x97, 0x68], [0xfd, 0x99, 0x69], [0xfd, 0x9b, 0x6a], [0xfd, 0x9d, 0x6b],

[0xfd, 0x9f, 0x6c], [0xfd, 0xa1, 0x6e], [0xfd, 0xa2, 0x6f], [0xfd, 0xa4, 0x70], [0xfe, 0xa6, 0x71], [0xfe, 0xa8, 0x73],

[0xfe, 0xaa, 0x74], [0xfe, 0xac, 0x75], [0xfe, 0xae, 0x76], [0xfe, 0xaf, 0x78], [0xfe, 0xb1, 0x79], [0xfe, 0xb3, 0x7b],

[0xfe, 0xb5, 0x7c], [0xfe, 0xb7, 0x7d], [0xfe, 0xb9, 0x7f], [0xfe, 0xbb, 0x80], [0xfe, 0xbc, 0x82], [0xfe, 0xbe, 0x83],

[0xfe, 0xc0, 0x85], [0xfe, 0xc2, 0x86], [0xfe, 0xc4, 0x88], [0xfe, 0xc6, 0x89], [0xfe, 0xc7, 0x8b], [0xfe, 0xc9, 0x8d],

[0xfe, 0xcb, 0x8e], [0xfd, 0xcd, 0x90], [0xfd, 0xcf, 0x92], [0xfd, 0xd1, 0x93], [0xfd, 0xd2, 0x95], [0xfd, 0xd4, 0x97],

[0xfd, 0xd6, 0x98], [0xfd, 0xd8, 0x9a], [0xfd, 0xda, 0x9c], [0xfd, 0xdc, 0x9d], [0xfd, 0xdd, 0x9f], [0xfd, 0xdf, 0xa1],

[0xfd, 0xe1, 0xa3], [0xfc, 0xe3, 0xa5], [0xfc, 0xe5, 0xa6], [0xfc, 0xe6, 0xa8], [0xfc, 0xe8, 0xaa], [0xfc, 0xea, 0xac],

[0xfc, 0xec, 0xae], [0xfc, 0xee, 0xb0], [0xfc, 0xf0, 0xb1], [0xfc, 0xf1, 0xb3], [0xfc, 0xf3, 0xb5], [0xfc, 0xf5, 0xb7],

[0xfb, 0xf7, 0xb9], [0xfb, 0xf9, 0xbb], [0xfb, 0xfa, 0xbd], [0xfb, 0xfc, 0xbf],

], dtype="uint8")

def mandelbrot(width: int, height: int, *,

x: float = -0.5, y: float = 0, zoom: int = 1, max_iterations: int = 100) -> np.array:

"""

From https://www.learnpythonwithrune.org/numpy-compute-mandelbrot-set-by-vectorization/.

"""

# To make navigation easier we calculate these values

x_width, y_height = 1.5, 1.5*height/width

x_from, x_to = x - x_width/zoom, x + x_width/zoom

y_from, y_to = y - y_height/zoom, y + y_height/zoom

# Here the actual algorithm starts

x = np.linspace(x_from, x_to, width).reshape((1, width))

y = np.linspace(y_from, y_to, height).reshape((height, 1))

c = x + 1j*y

# Initialize z to all zero

z = np.zeros(c.shape, dtype=np.complex128)

# To keep track in which iteration the point diverged

div_time = np.zeros(z.shape, dtype=int)

# To keep track on which points did not converge so far

m = np.full(c.shape, True, dtype=bool)

for i in range(max_iterations):

z[m] = z[m]**2 + c[m]

diverged = np.greater(np.abs(z), 2, out=np.full(c.shape, False), where=m) # Find diverging

div_time[diverged] = i # set the value of the diverged iteration number

m[np.abs(z)> 2] = False # to remember which have diverged

return div_time

def julia(width: int, height: int, *,

c: complex = -0.4 + 0.6j, x: float = 0, y: float = 0, zoom: int = 1, max_iterations: int = 100) -> np.array:

"""

From https://www.learnpythonwithrune.org/numpy-calculate-the-julia-set-with-vectorization/.

"""

# To make navigation easier we calculate these values

x_width, y_height = 1.5, 1.5*height/width

x_from, x_to = x - x_width/zoom, x + x_width/zoom

y_from, y_to = y - y_height/zoom, y + y_height/zoom

# Here the actual algorithm starts

x = np.linspace(x_from, x_to, width).reshape((1, width))

y = np.linspace(y_from, y_to, height).reshape((height, 1))

z = x + 1j*y

# Initialize z to all zero

c = np.full(z.shape, c)

# To keep track in which iteration the point diverged

div_time = np.zeros(z.shape, dtype=int)

# To keep track on which points did not converge so far

m = np.full(c.shape, True, dtype=bool)

for i in range(max_iterations):

z[m] = z[m]**2 + c[m]

m[np.abs(z)> 2] = False

div_time[m] = i

return div_time

def create_canvas(width: int, height: int, target: str) -> Context2d:

pixel_ratio = devicePixelRatio

Magma256=np.array([

[0x00,0x00,0x03], [0x00,0x00,0x04], [0x00,0x00,0x06], [0x01,0x00,0x07],

[0x01,0x01,0x09], [0x01,0x01,0x0b], [0x02,0x02,0x0d], [0x02,0x02,0x0f],

[0x03,0x03,0x11], [0x04,0x03,0x13], [0x04,0x04,0x15], [0x05,0x04,0x17],

[0x06,0x05,0x19], [0x07,0x05,0x1b], [0x08,0x06,0x1d], [0x09,0x07,0x1f],

[0x0a,0x07,0x22], [0x0b,0x08,0x24], [0x0c,0x09,0x26], [0x0d,0x0a,0x28],

[0x0e,0x0a,0x2a], [0x0f,0x0b,0x2c], [0x10,0x0c,0x2f], [0x11,0x0c,0x31],

[0x12,0x0d,0x33], [0x14,0x0d,0x35], [0x15,0x0e,0x38], [0x16,0x0e,0x3a],

[0x17,0x0f,0x3c], [0x18,0x0f,0x3f], [0x1a,0x10,0x41], [0x1b,0x10,0x44],

[0x1c,0x10,0x46], [0x1e,0x10,0x49], [0x1f,0x11,0x4b], [0x20,0x11,0x4d],

[0x22,0x11,0x50], [0x23,0x11,0x52], [0x25,0x11,0x55], [0x26,0x11,0x57],

[0x28,0x11,0x59], [0x2a,0x11,0x5c], [0x2b,0x11,0x5e], [0x2d,0x10,0x60],

[0x2f,0x10,0x62], [0x30,0x10,0x65], [0x32,0x10,0x67], [0x34,0x10,0x68],

[0x35,0x0f,0x6a], [0x37,0x0f,0x6c], [0x39,0x0f,0x6e], [0x3b,0x0f,0x6f],

[0x3c,0x0f,0x71], [0x3e,0x0f,0x72], [0x40,0x0f,0x73], [0x42,0x0f,0x74],

[0x43,0x0f,0x75], [0x45,0x0f,0x76], [0x47,0x0f,0x77], [0x48,0x10,0x78],

[0x4a,0x10,0x79], [0x4b,0x10,0x79], [0x4d,0x11,0x7a], [0x4f,0x11,0x7b],

[0x50,0x12,0x7b], [0x52,0x12,0x7c], [0x53,0x13,0x7c], [0x55,0x13,0x7d],

[0x57,0x14,0x7d], [0x58,0x15,0x7e], [0x5a,0x15,0x7e], [0x5b,0x16,0x7e],

[0x5d,0x17,0x7e], [0x5e,0x17,0x7f], [0x60,0x18,0x7f], [0x61,0x18,0x7f],

[0x63,0x19,0x7f], [0x65,0x1a,0x80], [0x66,0x1a,0x80], [0x68,0x1b,0x80],

[0x69,0x1c,0x80], [0x6b,0x1c,0x80], [0x6c,0x1d,0x80], [0x6e,0x1e,0x81],

[0x6f,0x1e,0x81], [0x71,0x1f,0x81], [0x73,0x1f,0x81], [0x74,0x20,0x81],

[0x76,0x21,0x81], [0x77,0x21,0x81], [0x79,0x22,0x81], [0x7a,0x22,0x81],

[0x7c,0x23,0x81], [0x7e,0x24,0x81], [0x7f,0x24,0x81], [0x81,0x25,0x81],

[0x82,0x25,0x81], [0x84,0x26,0x81], [0x85,0x26,0x81], [0x87,0x27,0x81],

[0x89,0x28,0x81], [0x8a,0x28,0x81], [0x8c,0x29,0x80], [0x8d,0x29,0x80],

[0x8f,0x2a,0x80], [0x91,0x2a,0x80], [0x92,0x2b,0x80], [0x94,0x2b,0x80],

[0x95,0x2c,0x80], [0x97,0x2c,0x7f], [0x99,0x2d,0x7f], [0x9a,0x2d,0x7f],

[0x9c,0x2e,0x7f], [0x9e,0x2e,0x7e], [0x9f,0x2f,0x7e], [0xa1,0x2f,0x7e],

[0xa3,0x30,0x7e], [0xa4,0x30,0x7d], [0xa6,0x31,0x7d], [0xa7,0x31,0x7d],

[0xa9,0x32,0x7c], [0xab,0x33,0x7c], [0xac,0x33,0x7b], [0xae,0x34,0x7b],

[0xb0,0x34,0x7b], [0xb1,0x35,0x7a], [0xb3,0x35,0x7a], [0xb5,0x36,0x79],

[0xb6,0x36,0x79], [0xb8,0x37,0x78], [0xb9,0x37,0x78], [0xbb,0x38,0x77],

[0xbd,0x39,0x77], [0xbe,0x39,0x76], [0xc0,0x3a,0x75], [0xc2,0x3a,0x75],

[0xc3,0x3b,0x74], [0xc5,0x3c,0x74], [0xc6,0x3c,0x73], [0xc8,0x3d,0x72],

[0xca,0x3e,0x72], [0xcb,0x3e,0x71], [0xcd,0x3f,0x70], [0xce,0x40,0x70],

[0xd0,0x41,0x6f], [0xd1,0x42,0x6e], [0xd3,0x42,0x6d], [0xd4,0x43,0x6d],

[0xd6,0x44,0x6c], [0xd7,0x45,0x6b], [0xd9,0x46,0x6a], [0xda,0x47,0x69],

[0xdc,0x48,0x69], [0xdd,0x49,0x68], [0xde,0x4a,0x67], [0xe0,0x4b,0x66],

[0xe1,0x4c,0x66], [0xe2,0x4d,0x65], [0xe4,0x4e,0x64], [0xe5,0x50,0x63],

[0xe6,0x51,0x62], [0xe7,0x52,0x62], [0xe8,0x54,0x61], [0xea,0x55,0x60],

[0xeb,0x56,0x60], [0xec,0x58,0x5f], [0xed,0x59,0x5f], [0xee,0x5b,0x5e],

[0xee,0x5d,0x5d], [0xef,0x5e,0x5d], [0xf0,0x60,0x5d], [0xf1,0x61,0x5c],

[0xf2,0x63,0x5c], [0xf3,0x65,0x5c], [0xf3,0x67,0x5b], [0xf4,0x68,0x5b],

[0xf5,0x6a,0x5b], [0xf5,0x6c,0x5b], [0xf6,0x6e,0x5b], [0xf6,0x70,0x5b],

[0xf7,0x71,0x5b], [0xf7,0x73,0x5c], [0xf8,0x75,0x5c], [0xf8,0x77,0x5c],

[0xf9,0x79,0x5c], [0xf9,0x7b,0x5d], [0xf9,0x7d,0x5d], [0xfa,0x7f,0x5e],

[0xfa,0x80,0x5e], [0xfa,0x82,0x5f], [0xfb,0x84,0x60], [0xfb,0x86,0x60],

[0xfb,0x88,0x61], [0xfb,0x8a,0x62], [0xfc,0x8c,0x63], [0xfc,0x8e,0x63],

[0xfc,0x90,0x64], [0xfc,0x92,0x65], [0xfc,0x93,0x66], [0xfd,0x95,0x67],

[0xfd,0x97,0x68], [0xfd,0x99,0x69], [0xfd,0x9b,0x6a], [0xfd,0x9d,0x6b],

[0xfd,0x9f,0x6c], [0xfd,0xa1,0x6e], [0xfd,0xa2,0x6f], [0xfd,0xa4,0x70],

[0xfe,0xa6,0x71], [0xfe,0xa8,0x73], [0xfe,0xaa,0x74], [0xfe,0xac,0x75],

[0xfe,0xae,0x76], [0xfe,0xaf,0x78], [0xfe,0xb1,0x79], [0xfe,0xb3,0x7b],

[0xfe,0xb5,0x7c], [0xfe,0xb7,0x7d], [0xfe,0xb9,0x7f], [0xfe,0xbb,0x80],

[0xfe,0xbc,0x82], [0xfe,0xbe,0x83], [0xfe,0xc0,0x85], [0xfe,0xc2,0x86],

[0xfe,0xc4,0x88], [0xfe,0xc6,0x89], [0xfe,0xc7,0x8b], [0xfe,0xc9,0x8d],

[0xfe,0xcb,0x8e], [0xfd,0xcd,0x90], [0xfd,0xcf,0x92], [0xfd,0xd1,0x93],

[0xfd,0xd2,0x95], [0xfd,0xd4,0x97], [0xfd,0xd6,0x98], [0xfd,0xd8,0x9a],

[0xfd,0xda,0x9c], [0xfd,0xdc,0x9d], [0xfd,0xdd,0x9f], [0xfd,0xdf,0xa1],

[0xfd,0xe1,0xa3], [0xfc,0xe3,0xa5], [0xfc,0xe5,0xa6], [0xfc,0xe6,0xa8],

[0xfc,0xe8,0xaa], [0xfc,0xea,0xac], [0xfc,0xec,0xae], [0xfc,0xee,0xb0],

[0xfc,0xf0,0xb1], [0xfc,0xf1,0xb3], [0xfc,0xf3,0xb5], [0xfc,0xf5,0xb7],

[0xfb,0xf7,0xb9], [0xfb,0xf9,0xbb], [0xfb,0xfa,0xbd], [0xfb,0xfc,0xbf],

],dtype="uint8")