dmishin

#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)

dmishin

"""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:

dmishin

#!/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"

dmishin

#!/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

dmishin

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):

dmishin

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

dmishin

#%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):

dmishin

$("#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);
    

dmishin

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:

dmishin

"""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