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numpy_canvas_fractals.html
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<html>
<head>
<title>
Visualization of Mandelbrot, Julia and Newton sets with NumPy and
HTML5 canvas
</title>
<meta charset="utf-8" />
<link rel="icon" type="image/x-icon" href="./favicon.png" />
<link
rel="stylesheet"
href="https://pyscript.net/latest/pyscript.css"
/>
<script defer src="https://pyscript.net/latest/pyscript.js"></script>
<link rel="stylesheet" href="./assets/css/examples.css" />
<style>
.loading {
display: inline-block;
width: 50px;
height: 50px;
border: 3px solid rgba(255, 255, 255, 0.3);
border-radius: 50%;
border-top-color: black;
animation: spin 1s ease-in-out infinite;
}
canvas {
display: none;
}
@keyframes spin {
to {
transform: rotate(360deg);
}
}
</style>
</head>
<body>
<nav class="navbar" style="background-color: #000000">
<div class="app-header">
<a href="/">
<img src="./logo.png" class="logo" />
</a>
<a class="title" href="" style="color: #f0ab3c"
>Fractals with NumPy and canvas</a
>
</div>
</nav>
<section class="pyscript">
<div
style="
display: flex;
flex-direction: column;
gap: 1em;
width: 600px;
"
>
<div id="mandelbrot">
<div style="text-align: center">Mandelbrot set</div>
<div>
<div class="loading"></div>
<canvas></canvas>
</div>
</div>
<div id="julia">
<div style="text-align: center">Julia set</div>
<div>
<div class="loading"></div>
<canvas></canvas>
</div>
</div>
<div id="newton">
<div style="text-align: center">Newton set</div>
<fieldset
style="display: flex; flex-direction: row; gap: 1em"
>
<div>
<span style="white-space: pre">p(z) = </span
><input
id="poly"
type="text"
value="z**3 - 2*z + 2"
/>
</div>
<div>
<span style="white-space: pre">a = </span
><input
id="coef"
type="text"
value="1"
style="width: 40px"
/>
</div>
<div style="display: flex; flex-direction: row">
<span style="white-space: pre">x = [</span>
<input
id="x0"
type="text"
value="-2.5"
style="width: 80px; text-align: right"
/>
<span style="white-space: pre">, </span>
<input
id="x1"
type="text"
value="2.5"
style="width: 80px; text-align: right"
/>
<span style="white-space: pre">]</span>
</div>
<div style="display: flex; flex-direction: row">
<span style="white-space: pre">y = [</span>
<input
id="y0"
type="text"
value="-5.0"
style="width: 80px; text-align: right"
/>
<span style="white-space: pre">, </span>
<input
id="y1"
type="text"
value="5.0"
style="width: 80px; text-align: right"
/>
<span style="white-space: pre">]</span>
</div>
<div
style="display: flex; flex-direction: row; gap: 1em"
>
<div style="white-space: pre">
<input
type="radio"
id="conv"
name="type"
value="convergence"
checked
/>
convergence
</div>
<div style="white-space: pre">
<input
type="radio"
id="iter"
name="type"
value="iterations"
/>
iterations
</div>
</div>
</fieldset>
<div>
<div class="loading"></div>
<canvas></canvas>
</div>
</div>
</div>
<py-tutor>
<py-config type="json">
{
"packages": [
"numpy",
"sympy"
],
"fetch": [
{
"files": [
"./palettes.py",
"./fractals.py"
]
}
],
"plugins": [
"https://pyscript.net/latest/plugins/python/py_tutor.py"
]
}
</py-config>
<py-script>
from pyodide.ffi import to_js, create_proxy
import numpy as np
import sympy
from palettes import Magma256
from fractals import mandelbrot, julia, newton
from js import (
console,
document,
devicePixelRatio,
ImageData,
Uint8ClampedArray,
CanvasRenderingContext2D as Context2d,
requestAnimationFrame,
)
def prepare_canvas(width: int, height: int, canvas: Element) -> Context2d:
ctx = canvas.getContext("2d")
canvas.style.width = f"{width}px"
canvas.style.height = f"{height}px"
canvas.width = width
canvas.height = height
ctx.clearRect(0, 0, width, height)
return ctx
def color_map(array: np.array, palette: np.array) -> np.array:
size, _ = palette.shape
index = (array/array.max()*(size - 1)).round().astype("uint8")
width, height = array.shape
image = np.full((width, height, 4), 0xff, dtype=np.uint8)
image[:, :, :3] = palette[index]
return image
def draw_image(ctx: Context2d, image: np.array) -> None:
data = Uint8ClampedArray.new(to_js(image.tobytes()))
width, height, _ = image.shape
image_data = ImageData.new(data, width, height)
ctx.putImageData(image_data, 0, 0)
width, height = 600, 600
async def draw_mandelbrot() -> None:
spinner = document.querySelector("#mandelbrot .loading")
canvas = document.querySelector("#mandelbrot canvas")
spinner.style.display = ""
canvas.style.display = "none"
ctx = prepare_canvas(width, height, canvas)
console.log("Computing Mandelbrot set ...")
console.time("mandelbrot")
iters = mandelbrot(width, height)
console.timeEnd("mandelbrot")
image = color_map(iters, Magma256)
draw_image(ctx, image)
spinner.style.display = "none"
canvas.style.display = "block"
async def draw_julia() -> None:
spinner = document.querySelector("#julia .loading")
canvas = document.querySelector("#julia canvas")
spinner.style.display = ""
canvas.style.display = "none"
ctx = prepare_canvas(width, height, canvas)
console.log("Computing Julia set ...")
console.time("julia")
iters = julia(width, height)
console.timeEnd("julia")
image = color_map(iters, Magma256)
draw_image(ctx, image)
spinner.style.display = "none"
canvas.style.display = "block"
def ranges():
x0_in = document.querySelector("#x0")
x1_in = document.querySelector("#x1")
y0_in = document.querySelector("#y0")
y1_in = document.querySelector("#y1")
xr = (float(x0_in.value), float(x1_in.value))
yr = (float(y0_in.value), float(y1_in.value))
return xr, yr
current_image = None
async def draw_newton() -> None:
spinner = document.querySelector("#newton .loading")
canvas = document.querySelector("#newton canvas")
spinner.style.display = ""
canvas.style.display = "none"
ctx = prepare_canvas(width, height, canvas)
console.log("Computing Newton set ...")
poly_in = document.querySelector("#poly")
coef_in = document.querySelector("#coef")
conv_in = document.querySelector("#conv")
iter_in = document.querySelector("#iter")
xr, yr = ranges()
# z**3 - 1
# z**8 + 15*z**4 - 16
# z**3 - 2*z + 2
expr = sympy.parse_expr(poly_in.value)
coeffs = [ complex(c) for c in reversed(sympy.Poly(expr, sympy.Symbol("z")).all_coeffs()) ]
poly = np.polynomial.Polynomial(coeffs)
coef = complex(sympy.parse_expr(coef_in.value))
console.time("newton")
iters, roots = newton(width, height, p=poly, a=coef, xr=xr, yr=yr)
console.timeEnd("newton")
if conv_in.checked:
n = poly.degree() + 1
k = int(len(Magma256)/n)
colors = Magma256[::k, :][:n]
colors[0, :] = [255, 0, 0] # red: no convergence
image = color_map(roots, colors)
else:
image = color_map(iters, Magma256)
global current_image
current_image = image
draw_image(ctx, image)
spinner.style.display = "none"
canvas.style.display = "block"
handler = create_proxy(lambda _event: draw_newton())
document.querySelector("#newton fieldset").addEventListener("change", handler)
canvas = document.querySelector("#newton canvas")
is_selecting = False
init_sx, init_sy = None, None
sx, sy = None, None
async def mousemove(event):
global is_selecting
global init_sx
global init_sy
global sx
global sy
def invert(sx, source_range, target_range):
source_start, source_end = source_range
target_start, target_end = target_range
factor = (target_end - target_start)/(source_end - source_start)
offset = -(factor * source_start) + target_start
return (sx - offset) / factor
bds = canvas.getBoundingClientRect()
event_sx, event_sy = event.clientX - bds.x, event.clientY - bds.y
ctx = canvas.getContext("2d")
pressed = event.buttons == 1
if is_selecting:
if not pressed:
xr, yr = ranges()
x0 = invert(init_sx, xr, (0, width))
x1 = invert(sx, xr, (0, width))
y0 = invert(init_sy, yr, (0, height))
y1 = invert(sy, yr, (0, height))
document.querySelector("#x0").value = x0
document.querySelector("#x1").value = x1
document.querySelector("#y0").value = y0
document.querySelector("#y1").value = y1
is_selecting = False
init_sx, init_sy = None, None
sx, sy = init_sx, init_sy
await draw_newton()
else:
ctx.save()
ctx.clearRect(0, 0, width, height)
draw_image(ctx, current_image)
sx, sy = event_sx, event_sy
ctx.beginPath()
ctx.rect(init_sx, init_sy, sx - init_sx, sy - init_sy)
ctx.fillStyle = "rgba(255, 255, 255, 0.4)"
ctx.strokeStyle = "rgba(255, 255, 255, 1.0)"
ctx.fill()
ctx.stroke()
ctx.restore()
else:
if pressed:
is_selecting = True
init_sx, init_sy = event_sx, event_sy
sx, sy = init_sx, init_sy
canvas.addEventListener("mousemove", create_proxy(mousemove))
import asyncio
async def main():
_ = await asyncio.gather(
draw_mandelbrot(),
draw_julia(),
draw_newton(),
)
asyncio.ensure_future(main())
</py-script>
</py-tutor>
</section>
</body>
</html>