NebulaRemix

Nebula Remix

🍏 Green Fog wallpaper, 🦜🎩 Try Mandelbrot Fractals!

A WebGL reconstruction of the recursive domain warping technique found in Android’s “Magic Smoke” live wallpaper.

It simulates fluid dynamics and cloud formations not through Navier-Stokes equations, but via iterated fractional Brownian motion (FBM), where the noise domain is distorted by the noise itself.

more retro-goods like Phase Beam、Bubble、Nexus、Water Ripple、Grass can be found in livewall.zip

Gallery

• 🧬c_life
• 🦢 Boids
• 💧 Liquid Glass, try Damp=.99, Brush large

normal phys(gravity sensors supported!):

• 🔴balls_bezier, Classic.
• 🔴balls… 🏀 Box 3D balls!, CG101: D2(x,y)(runs,turn) func
• 👠Constraint P/Link
• 🍥fft XYs2rhoTaus, (Eq. used)
• 🖥cmatrix, 👍 GUI+TUI Game 2048
• 🧷box_bezier, 👍 Sandboxels

field:

• 💦JS Water & Our Holo Cosmos(3): ☯️！ 🍩！ 👑！
• ⏳c_sand, heat_death
• 💈hair_style (MouseR), 👍 xyz Voxels(Minecraft)
• 🏙van_gogh: Starry night
• 🏙van_sfx: Math-ic carpet

field(hard):

• Vid: Clothes/Jelly 🎄 Blob Opera
• 💦flow, 👍 WASM phys, 🎄 XMas tree/z-index
• Clothes & 👕 ⛈Live2D/Piecewise-Affine trans drop a image, mid-click!

See Also

• Inigo Quilez: Domain Warping - The foundational article on this technique.
• The Book of Shaders: Fractal Brownian Motion - Visual guide to noise layering.
• Curl Noise - An alternative approach for divergence-free fluid simulation.
• CURL Noise function

Zen Algorithm

Sorting Vis (Text mode) 玩法：tap【记录】，tap播放。

Vid: Stalin & PNG bars sort, With sound + 🐧 Gogo Giegie

• 🧷 Trie URL/Dict tokenizer & basenc --help impl 逆波兰带步骤计算器、Trie后缀压缩树、cubic-bezier()，这些拓扑排序（可视化）日用算法
• 🤖 文字探索游戏 单字ngram kNN平滑混乱文本生成（输入法算法）
• 📚 Good First DSP - 禅 👍👍👍

^ tutour (PPT)

Game-Life

ASCII Art

Cool 📊 PoV display, Holographic Volume, Open Menu&”Apply”, idShape=SDF Voxel

# ipy Ctrl-K image viewer
import os, cv2, numpy as np
grays = [*" .-:=*+%@#"]
def ascii(img, wh=np.int32(os.popen('stty size', 'r').read().split()[::-1])  ):
  g=np.array(grays)
  a=cv2.cvtColor(cv2.resize(img, wh) , cv2.COLOR_BGR2GRAY)
  b=np.int8(np.interp(a, (0,256), (0,len(g)) ))
  return [*
    (''.join(y) for y in g[b] )
  ]

@get_ipython().pt_app.key_bindings.add('c-k')
def f(ev):
  s=os.popen('ls -t ~/Pictures/Screenshots/* | head -n 1').read().strip()
  print(*ascii(cv2.imread(s)), sep="\n")

# Heart anim
import os, cv2, time
from numpy import*

Nm=array; mix=interp
sh=lambda s: os.popen(s).read()[:-1]

def heart(P, k=.8):
  t = mix(mod(iTime, k), [0, k], [0.3, k])  # Heartbeat
  r = (P[1] - power(abs(P[0]), t))**2 + P[0]**2 - 1.0  # Grayscale function
  return where(r < 0.3, mix(-r, [0, 0.3], [1, 4]), r)

grays = Nm([*" .-:", '\x1B[1;31m=\x1B[0m', *"+*%@#"])
GL=lambda w,h: Nm(meshgrid(linspace(0,1, w), linspace(1,0, h)))

def drawBW(g, wh=flip(int32(sh('stty size').split())), bg=grays):
  a=(1-g(GL(*wh)*5-2-sin(iTime)))*256 if callable(g) else cv2.cvtColor(cv2.resize(g, wh) , cv2.COLOR_BGR2GRAY)
  b=int8(mix(a, (0,256), (0,len(bg)-1) ))
  print('\x1B[0;0H', '\n'.join(''.join(y) for y in bg[b] ))

try: #.: ipy -i
  @get_ipython().pt_app.key_bindings.add('c-k')
  def cropBW(F5):
    g=cv2.imread(sh('zenity --file-selection'))
    drawBW(g)
except:
  for iTime in (x/100 for x in range(0, 600)): drawBW(heart); time.sleep(1/60)

FBm

Logic projection of the “Magic Smoke” shader’s main() loop.

• Recursive FBM (numpy-cpu notebook)
• that .zip: Android Live Wallpapers

import numpy as np
import matplotlib.pyplot as plt

def noise(p):
  # Grid coords & fractional offsets
  i = np.floor(p).astype(int); f = p - i
  f = f*f*(3 - 2*f) # Hermite smoothing
  
  # Hashing logic (Vectorized py random)
  def h(c):
    return (np.sin(c[...,0]*12.9898 + c[...,1]*78.233) * 43758.5453) % 1

  # Bilinear interpolation across the 4 corners
  a, b = h(i), h(i + [1,0])
  c, d = h(i + [0,1]), h(i + [1,1])
  
  return a + (b-a)*f[...,0] + (c-a)*f[...,1] + (a-b-c+d)*f[...,0]*f[...,1]

def fbm(p, octaves=6):
  v, amp = 0, .5
  for _ in range(octaves):
    v += amp * noise(p); p *= 2.; amp *= .5
  return v

def warp(p, t):
  # q = f(p + d1)
  q = np.stack([fbm(p + t), fbm(p + t + 5.2)], axis=-1)
  # r = f(p + 4q + d2)
  r = np.stack([fbm(p + 4*q + 1.7), fbm(p + 4*q + 9.2)], axis=-1)
  # smokeFlavor = f(p + 4r)
  return fbm(p + 4*r)

# Execute
res = 256
x = np.linspace(0, 5, res)
grid = np.stack(np.meshgrid(x, x), axis=-1)
img = warp(grid, 0.5)

plt.imshow(img, cmap='magma', origin='lower')
plt.axis('off')
plt.show()

Have fun!

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