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#Requires: numpy, PIL | |
from fractions import gcd | |
from numpy import array, meshgrid, frompyfunc, clip, histogram | |
from numpy.fft import fft2 | |
import numpy as np | |
from PIL import Image | |
def value_diapason(x, percent=0.95, nbins=100): | |
"""Use histogram to determine area, covering 95% of values""" | |
counts, bins = histogram(x.ravel(),nbins) |
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"""Experiments with the 'sumsin' function: maximization and plotting | |
S(x) = sin(x) + sin(2x)/2 + sin(4x)/4 + ... | |
it appears that S(x) reaches maximum at | |
xmax = 0.8905302010175791857059461558*7027* | |
whereas | |
36pi/127=0.8905302010175791857059461558*9025* | |
Plots of the function: |
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#!/usr/bin/env python | |
#This is Python3 executable | |
import os.path | |
from numpy import array, hstack, vstack, clip | |
from PIL import Image | |
import numpy as np | |
import subprocess | |
import re | |
#SOX_EXEC = r"C:\Program Files\sox-14-4-2\sox.exe" |
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#!/usr/bin/env python | |
from __future__ import print_function, division | |
import os.path | |
from numpy import array, hstack, vstack, clip | |
from PIL import Image | |
import numpy as np | |
import subprocess # need the subprocess module | |
from tempfile import mkdtemp | |
import shutil |
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def approxfi(x, n): | |
#Apply x -> F(x) mapping until x is sufficiently large | |
k = 0 | |
while (x < 1e14) and (k<100): | |
x = x**2-2 | |
k += 1 | |
#Calculate approximate fractional iterate for large argument | |
x = x**(2**n) | |
#Apply reverse mapping x -> F[-1](x) | |
for _ in range(k): |
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import numpy as np | |
import scipy as sp | |
import scipy.linalg | |
from math import floor, pi | |
#Detect optimal step for minimal order Schreiber test signal | |
#Set to False to disable printing | |
_verbose = True |
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#%metadata% | |
#url: https://twitter.com/diegorattaggi/status/1252654580720119810/photo/1 | |
from sympy import * | |
mfib = Matrix([[0,1],[1,1]]) | |
fib0 = Matrix([0,1]) | |
luc0 = Matrix([2,1]) | |
eye = Matrix([[1,0],[0,1]]) | |
def fibo(n): |
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$("#run").click(() => tryCatch(run)); | |
async function run() { | |
Excel.run(async function (context) { | |
var sctivesheet = context.workbook.worksheets.getActiveWorksheet(); | |
var table = sctivesheet.tables.add(sctivesheet.getRangeByIndexes(0, 0, 1, 2), true); | |
var data = [[1, "A"], [2, "B"], [3, "C"]]; | |
table.rows.add(0, data); | |
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import numpy as np | |
from matplotlib import pyplot as plt | |
import scipy | |
def ht(n:int)->np.array: | |
"""Generates Thue-Morse sequence, arranged along the Hilbert curve of order N. Result is (2**n, 2**n) matrix""" | |
if n < 0: raise ValueError("Bad order") | |
if n == 0: | |
return np.array([[1]], dtype=np.int8) | |
else: |
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"""Calculate smooth iterates of the function | |
f:[0,1]->[0,1] | |
f(x) = 1-sqrt(1-x^2) | |
https://mathoverflow.net/questions/449748/what-are-the-iterates-of-x-mapsto-1-sqrt1-x2 | |
https://twitter.com/gro_tsen/status/1674132770203881477 | |
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