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So I have generated this simple height map to test my add on: enter image description here

That's the node setup and the result that I am having in Blender: enter image description here

What is happening here (basically, that's a theory, I did not analyze the actual pixel values programmatically): Blender Bump node is interpreting each slightest variation in the pixel value (say, 0.985 white and 0.99 white) as variation in height. What you have as a result are the ugly cutoffs. By the way, a similar question with the same problem, unsolved: height map brings weird result

Now, if I do converting in CrazyBump, I have the opportunity to ignore small details, and, if I convert with CrazyBump, the map is displayed correctly in blender. By their nature, any height map, even 16K will not be absolutely smooth because the set of possible heights is a set of discrete values, it will never be smooth. The task of an algo would be to produce smooth normals from this. And this is what Bump node obviously does not do. Any suggestions? (using other software does not work, I want to achieve it specifically in the node editor of Blender, for any BW map)

and just to prove the point: if I twick the small details all the way up in CrazyBump, I will get essentially what the BumpNode in Blender is doing: overexaggerating non-significant value variations: enter image description here

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    $\begingroup$ It might have to do with the bit depth of the height map. 8 bit images are not enough to resolve subtle gradation. Try using images in a higher bit depth. Also, images used for bumps and normals should not be interpreted as color, but as Non-Color-Data (linear) $\endgroup$ – user1853 Mar 23 '19 at 17:39
  • $\begingroup$ @cegaton thanks for responding. bpy.data.images['...'].depth tells me it's 32 bit depth (is this the right indicator?). Also, changing to non-color does not affect the result. take a look at the last illustration: CrazyBump can algorithmically ignore or exaggerate those cuttoffs by setting its degree of attention to fine details $\endgroup$ – SerhiiPoklonskyi Mar 23 '19 at 17:47
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    $\begingroup$ 32 bit is 8bit per channel+Alpha (8 bit x 4). Try creating the image as a 16 bit per channel file. Non-color data should always be used for bump and height maps to avoid the distortion caused by the 2.2 gamma curve used in image encoded in sRGB. You might get better results using a displace modifer and subsurf than using displacement in the material or shader. $\endgroup$ – user1853 Mar 23 '19 at 17:50
  • $\begingroup$ @cegaton holy Jesus! it has solved the problem! marry me, cegaton! I totally agree with you with regard to displacement but my idea was to combine individual alpha elements to produce reliefs and cravings easily. now it will work thanks to you. if you so wish, post an answer for others, probably with a bit of explanation on depth and how it affects the result $\endgroup$ – SerhiiPoklonskyi Mar 23 '19 at 18:09
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short answer: as @cegaton has pointed out, save your image with 16 bits depth. If you are baking like me, this has to be done before bake, because resaving later does not generate information lost while baking. Go to 'Save as' dialog, there in the lower left corner choose 16 bits depth.

A (not so) technical explanation: if you are not familiar, depth is the number of bits used to store the pixel color. With 8 bits, you store 2^8 = 256 color values at maximum, with 16 bits that's 2^16 = 65536 possible colors. What was happening in my case is the following: for the different height values in the geometry that I was baking, an approximation was generated to store the height. In other words, for heights x-0.01, x, x+0.01s, it would simply put x, because it has no bits to store all the three. Hence the flat areas in your image, where the color gets 'simplified'. For my 8 bits image, I did for learning purposes:

len(set(bpy.data.images['My8BitImg.png'].pixels))

This has returned 256, while 

len(set(bpy.data.images['My16BitImg.png'].pixels))

has returned 42891 in my case.

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