Test Points as Pixels.ipynb

Kernel: Python 3 (system-wide)

Test Points as Pixels and Shade

import numpy as np
import imageio
from PIL import Image
import math
from numba import njit

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-1-468c2947ab96> in <module>
      3 from PIL import Image
      4 import math
----> 5 from numba import njit

~/.local/lib/python3.6/site-packages/numba/__init__.py in <module>
     43 
     44 # Initialize typed containers
---> 45 import numba.typed
     46 
     47 # Keep this for backward compatibility.
~/.local/lib/python3.6/site-packages/numba/typed/__init__.py in <module>
      1 from __future__ import absolute_import
      2 
----> 3 from .typeddict import Dict
      4 from .typedlist import List
~/.local/lib/python3.6/site-packages/numba/typed/typeddict.py in <module>
     16 
     17 
---> 18 @njit
     19 def _make_dict(keyty, valty):
     20     return dictobject._as_meminfo(dictobject.new_dict(keyty, valty))
~/.local/lib/python3.6/site-packages/numba/decorators.py in njit(*args, **kws)
    222         warnings.warn('forceobj is set for njit and is ignored', RuntimeWarning)
    223     kws.update({'nopython': True})
--> 224     return jit(*args, **kws)
    225 
    226 
~/.local/lib/python3.6/site-packages/numba/decorators.py in jit(signature_or_function, locals, target, cache, pipeline_class, **options)
    159                    targetoptions=options, **dispatcher_args)
    160     if pyfunc is not None:
--> 161         return wrapper(pyfunc)
    162     else:
    163         return wrapper
~/.local/lib/python3.6/site-packages/numba/decorators.py in wrapper(func)
    175         disp = dispatcher(py_func=func, locals=locals,
    176                           targetoptions=targetoptions,
--> 177                           **dispatcher_args)
    178         if cache:
    179             disp.enable_caching()
~/.local/lib/python3.6/site-packages/numba/dispatcher.py in __init__(self, py_func, locals, targetoptions, impl_kind, pipeline_class)
    574         """
    575         self.typingctx = self.targetdescr.typing_context
--> 576         self.targetctx = self.targetdescr.target_context
    577 
    578         pysig = utils.pysignature(py_func)
~/.local/lib/python3.6/site-packages/numba/targets/registry.py in target_context(self)
     48             return nested
     49         else:
---> 50             return self._toplevel_target_context
     51 
     52     @property
~/.local/lib/python3.6/site-packages/numba/utils.py in __get__(self, instance, type)
    379         if instance is None:
    380             return self
--> 381         res = instance.__dict__[self.name] = self.func(instance)
    382         return res
    383 
~/.local/lib/python3.6/site-packages/numba/targets/registry.py in _toplevel_target_context(self)
     32     def _toplevel_target_context(self):
     33         # Lazily-initialized top-level target context, for all threads
---> 34         return cpu.CPUContext(self.typing_context)
     35 
     36     @utils.cached_property
~/.local/lib/python3.6/site-packages/numba/targets/base.py in __init__(self, typing_context)
    248 
    249         # Initialize
--> 250         self.init()
    251 
    252     def init(self):
~/.local/lib/python3.6/site-packages/numba/compiler_lock.py in _acquire_compile_lock(*args, **kwargs)
     30         def _acquire_compile_lock(*args, **kwargs):
     31             with self:
---> 32                 return func(*args, **kwargs)
     33         return _acquire_compile_lock
     34 
~/.local/lib/python3.6/site-packages/numba/targets/cpu.py in init(self)
     47     def init(self):
     48         self.is32bit = (utils.MACHINE_BITS == 32)
---> 49         self._internal_codegen = codegen.JITCPUCodegen("numba.exec")
     50 
     51         # Add ARM ABI functions from libgcc_s
~/.local/lib/python3.6/site-packages/numba/targets/codegen.py in __init__(self, module_name)
    610         self._llvm_module.name = "global_codegen_module"
    611         self._rtlinker = RuntimeLinker()
--> 612         self._init(self._llvm_module)
    613 
    614     def _init(self, llvm_module):
~/.local/lib/python3.6/site-packages/numba/targets/codegen.py in _init(self, llvm_module)
    619         self._tm_features = self._customize_tm_features()
    620         self._customize_tm_options(tm_options)
--> 621         tm = target.create_target_machine(**tm_options)
    622         engine = ll.create_mcjit_compiler(llvm_module, tm)
    623 
TypeError: create_target_machine() got an unexpected keyword argument 'jitdebug'

class shade(object):
    def __init__(self, testFunction, bounds=(-1,1,-1,1), dpi=72, backgroundColor=(0,0,0)):
        self.testFunction = testFunction
        self.backgroundColor = backgroundColor
        self.dpi = dpi ## Is there a better way to do the dpi?
        self.xmin, self.xmax, self.ymin, self.ymax = bounds
        self.bounds = (self.xmin, self.xmax, self.ymin, self.ymax)
        self.width = math.ceil((self.xmax-self.xmin) * self.dpi)
        self.height = math.ceil((self.ymax-self.ymin) * self.dpi)
        self.pic = Image.new('RGB', (self.width, self.height), self.backgroundColor)
        self.pixels = self.pic.load()
        self.h = 0
        self.k = 0

    def _scale_to_plane(self, h, k):
        x = self.xmin + h * (self.xmax-self.xmin) / self.width
        y = self.ymax - k * (self.ymax-self.ymin) / self.height
        return x, y

    def fill(self):
        while self.h < self.width:
            while self.k < self.height:
                self.pixels[self.h,self.k] = self.testFunction(*self._scale_to_plane(self.h,self.k))
                self.k += 1
            self.h += 1
            self.k = 0

    def save_pic(self, path='Trash.png'):
        self.pic.save(path)

Simple

def d(a,b):
    return np.sqrt((a[0]-b[0])**2 + (a[1]-b[1])**2)

def simple(x, y):
    if d((x,y), (0,0)) <= 1:
        return (255, 255, 255)
    else:
        return (0,0,0)

simple = shade(simple)
simple.fill()
simple.pic

ALA

def lbda(a,b):
    return (a+np.sqrt(a**2+2*b))/2

def notToZero(a,b):
    if (np.linalg.matrix_power(np.array([[a,b],[1/2,0]]),10)>10).any():
        return True
    else:
        return False

def ala(a, b):
    if notToZero(a,b):
        return (255, 255, 255)
    else:
        return (0,0,0)

ALA = shade(ala, bounds=(0,5,0,5))
ALA.fill()
ALA.pic

Mandelbrot

# @njit
def mandelbrotTest(x_0, y_0):
    x, y = x_0, y_0

    # Check for in the first bulb
    q = (x - 1/4)**2 + y**2
    if q * ( q + (x - 1/4)) <= y**2/4:
        return (0,0,0)

    # check for 2nd bulb
    if (x + 1)**2 + y**2 <= 1/16:
        return (0,0,0)

    # really outside
    if x**2 + y**2 >= 4:
        return (0,0,255)

    # iterations
    for i in range(100000):
        x, y = x**2 - y**2 + x_0, 2 * x * y + y_0
        if x**2 + y**2 >= 4:
            return mandelbrotColor(i + 1)
    return (0,0,0)


# @njit
def mandelbrotColor(i):
    if i == -1:
        return (0,0,0)
    red = max(20 * abs((i - 25.5) % 38.25 - 19.125) - 127.5, 0)
    green = max(20 * abs((i - 12.75) % 38.25 - 19.125) - 127.5, 0)
    blue = max(20 * abs(i % 38.25 - 19.125) - 127.5, 0)
    return (int(red), int(green), int(blue))

mand = shade(mandelbrotTest, dpi=72, bounds=(-2.25, 2.25, -2.25, 2.25))  #

mand.fill()

mand.pic

Weird Lanscape

abs(x**y) < abs(y % x)
abs(x % y) < abs(x**y)
abs(y**x) < abs(y%x)
abs(x**x) < abs(x**y + y**x) and abs(y**y) > abs(x**y + y**x)

def cool(x, y):
    if y == 0 or x==0:
        return (255, 0 ,0)
    if abs(x % y) < abs(x**y) and abs(x**y) < abs(y % x):
        return (255,255,255)
    else:
        return (0,0,0)

new = shade(cool, dpi=100, bounds = (-10,10,-10,10))
new.fill()
new.pic

Different

@njit
def diffTest(x_0, y_0):
    x, y = x_0, y_0

    # iterations
    for i in range(100000):
        x, y = x**2 - y**2, 2 * x * y - .8
        if x**2 + y**2 >= 10:
            return mandelbrotColor(i + 1)
    return (0,0,0)

diff = shade(diffTest, dpi=75, bounds=(-2.25, 2.25, -2.25, 2.25))  # bounds = (-.25,0,.75,1))   #

diff.fill()

diff.pic

mand like

@njit
def mandLike(x_0, y_0):
    x, y = x_0, y_0

    # iterations
    for i in range(100000):
        x, y = x**x_0, y**y_0
        if x**2 + y**2 >= 10:
            return (255,255,255)  madLikeColor(i + 1)
    return (0,0,0)


@njit
def mandLikeColor(i):
    if i == -1:
        return (0,0,0)
    red = max(20 * abs((i - 25.5) % 38.25 - 19.125) - 127.5, 0)
    green = max(20 * abs((i - 12.75) % 38.25 - 19.125) - 127.5, 0)
    blue = max(20 * abs(i % 38.25 - 19.125) - 127.5, 0)
    return (int(red), int(green), int(blue))

  File "<ipython-input-11-532ee8634d66>", line 9
    return (255,255,255)  madLikeColor(i + 1)
                                     ^
SyntaxError: invalid syntax

like = shade(mandLike, dpi=50, bounds = (-10,10,-10,10))
like.fill()

---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
<ipython-input-12-4c24182b474e> in <module>()
      1 like = shade(mandLike, dpi=50, bounds = (-10,10,-10,10))
----> 2 like.fill()

<ipython-input-2-e1cf7f3db49b> in fill(self)
     21         while self.h < self.width:
     22             while self.k < self.height:
---> 23                 self.pixels[self.h,self.k] = self.testFunction(*self._scale_to_plane(self.h,self.k))
     24                 self.k += 1
     25             self.h += 1
KeyboardInterrupt: 

like.pic