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Tetration Fractal.

Python, 30 lines
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30``` ```# Tetration Fractal # http://en.wikipedia.org/wiki/Tetration # FB - 201110237 import math from PIL import Image imgx = 512 imgy = 512 image = Image.new("RGB", (imgx, imgy)) # drawing area (xa < xb & ya < yb) xa = -1.5 xb = -0.75 ya = 0.0 yb = 0.75 maxIt = 256 # max number of iterations allowed for ky in range(imgy): for kx in range(imgx): x = xa + (xb - xa) * kx / (imgx - 1) y = ya + (yb - ya) * ky / (imgy - 1) for i in range(maxIt): try: e = math.exp(-0.5 * math.pi * y) p = math.pi * x / 2 x = e * math.cos(p) y = e * math.sin(p) except: break if math.hypot(x, y) > 1000000: break image.putpixel((kx, ky), (i % 4 * 64, i % 8 * 32, i % 16 * 16)) image.save("TetrationFractal.png", "PNG") ``` FB36 (author) 11 years, 3 months ago
``````# Tetration Calculator
# http://en.wikipedia.org/wiki/Tetration
# FB - 201110237
import math
# Tetration by Linear Approximation
def Tetration_LA(a, x):
if x <= -1:
return math.log(Tetration_LA(a, x + 1), a)
if -1 < x and x <= 0:
return 1 + x
if 0 < x:
return math.pow(a, Tetration_LA(a, x - 1))

# Test
print Tetration_LA(math.e, 0.5 * math.pi)
print Tetration_LA(0.5, -4.3)
print Tetration_LA(math.pi, 0.5 * math.e)
`````` FB36 (author) 11 years, 3 months ago

Basic arithmetic operations (addition, multiplication, power) are actually first 3 of a general operation sequence. Tetration is the 4th, pentation is the 5th. Created by FB36 on Mon, 24 Oct 2011 (MIT)