A simple way to visualize what is happening is with UCSF ChimeraX. You can use 
the gaussian filter function to select either the frown or the smile from the 
“hidden_frown.map”, and then you can visualize the FFT structure factor 
magnitudes for each one – here are the commands to do it -

open hidden_frown.map
vol  gaussian #1 sdev 0.5
vol  gaussian #1 sdev 0.5 inv true
vol fourier #1
vol fourier #2
vol fourier #3

Fun stuff- your example is a great way of illuminating what is going on with 
filtering and fourier transforms!

Cheers, Chuck

From: CCP4 bulletin board <[email protected]> on behalf of James Holton 
<[email protected]>
Date: Sunday, April 30, 2023 at 5:16 PM
To: [email protected] <[email protected]>
Subject: Re: [ccp4bb] happy/sad maps
Thank you Paul.  This is interesting!

I have not played with super-sampling yet.  I am assuming you mean
creating a new map 8x the size? If so, did you fill the interstitial
grid with zeroes? Local maximum? Linear interpolation?  Tricubic spline?

And when you say "sharpen/blur" with a factor of 4. Is 4 a scale factor?
or a B factor?

Cheers, and I hope you had a pleasant weekend,

-James

On 4/28/2023 5:29 PM, Paul Emsley wrote:
> What fun!
>
> super-sampled by a factor of 2 then sharpen/blur with a factor of 4
> gives a superposition
>
> Paul.
>

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