# Creating visually random images

How complicated does a mathematical function, pseudorandom(x), have to be to create something that seems random, and how do you check whether it seems random? Looking at a long list of numbers is not a good way, because our ability to look at long lists of numbers is very limited. Our ability to look at images is much better.

So, to inspect whether a list of numbers is seemingly random, a fun way is to create an image using the numbers for each pixel, and simply look at it.

Given a number x in the series {0, 1, 2, …, huge n}, let’s create an image that plots a random function that’s implemented using the sin() function and a 3rd degree polynomial function:

```color_range = 2**8
a = -3.0
b = -5.0
c = 13.0

def pseudo_randombit(x):
color255 = math.sin(a*x**3 + b*x**2 + c*x) % color_range
# make black/white
bit = color255 / 127
return bit
```

I’m no signal processing expert, but his approach intuitively seems similar to distortion. Create a big number and make it fit inside a small room, throwing sin() into the mix for to make the number flip between positive and negative number. Note: I should refine the function given this realization, and simply check the sign…

The full example that uses GDAL (sinpol3_raster.py). Nevermind the geographical projection stuff, I copy-pasted some code, sorry:

```import osr
import numpy
import gdal
import math
import sys

color_range = 2**8
a = -3.0
b = -5.0
c = 13.0

def pseudo_randombit(x):

color255 = math.sin(a*x**3 + b*x**2 + c*x) % color_range
# make black/white
bit = color255 / 127
return bit

def main(argv):

width = int(argv)
height = int(argv)

format = "GTiff"
driver = gdal.GetDriverByName( format )

dst_ds = driver.Create( "sinpol3.tif", width, height, 1, gdal.GDT_Byte )

dst_ds.SetGeoTransform( [ 444720, 30, 0, 3751320, 0, -30 ] )

srs = osr.SpatialReference()
srs.ImportFromEPSG(25832)
dst_ds.SetProjection( srs.ExportToWkt() )

raster = numpy.zeros( (height, width), dtype=numpy.uint32 )

for x in range(0, height*width-1):

bit = pseudo_randombit(x)
# make black/white
color = bit * 255
i = (x / width)
j = x % width
raster[i][j] = color

dst_ds.GetRasterBand(1).WriteArray( raster )

if __name__ == '__main__':
main(sys.argv)
```

Calling sinpol3_raster.py:

```\$ python sinpol3_raster.py 500 500
\$ ls *.tif
sinpol3.tif
```

sinpol3.tif: Close-up of sinpol3.tif: An idea that takes this idea further is cryptographic QR-codes… Is the pseudo-random function given above directly reversible? I have to think about this. But now I have other matters to attend to, like a phd in high-availability geospatial services.

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