How to make figures in a casual, old-fashioned style

Question

I'm writing a math textbook and use Mathematica to make figures. However, like all modern software, Mathematica produces perfectly crisp mathematically accurate figures. Meanwhile, I feel that old-fashioned figures from books that predate computers are in some ways better for educational purposes as they appear less cold and sterile. See, for example, the figure below.

I'm sure that part of the style is due to loss of quality due to compression. However, I'm fairly confident that those curves are mathematically inaccurate, i.e. "casual".

I'm sure I can make my figures 1% inaccurate so that's not an issue. I'm wonder if there is a way to "stroke" the lines to give them that more casual look. Also, I open to any other suggestion for making my Mathematica figures more effective for educational purposes.

Answer 1

If you want grungy diagrams, you could always pass your graphics through JPEG export at a high level of compression, then re-import:

img = Rasterize[Graphics[{Thick, FaceForm[None], EdgeForm[Thick],
     Circle[],
     Rectangle[{-.3, .25}, {0, .7}, RoundingRadius -> .05],
     Text[
      Style["любовь.", FontSize -> 36, FontFamily -> "Courier", 
       FontWeight -> Bold], {-.5, .1}],
     Arrow[{{-1, -1}, {1, 1}}], 
     BezierCurve[{{-1, -1}, {.8, -.8}, {.9, .8}}]
     }], RasterSize -> {256, 256}];

imgexp = ExportString[img, "JPEG", "CompressionLevel" -> .8];
GaussianFilter[
 Binarize@ImageResize[ImportString[imgexp, "JPEG"], {512, 512}], 2]

You can apply the effect to other Plot diagrams too and the result is actually quite aesthetically pleasing:

img = Rasterize[Plot[{Sin[8 Pi x] x, x, -x}, {x, 0, 1}], 
   RasterSize -> {480, 320}];
img = ImageAdd[img, RandomImage[.25, ImageDimensions[img]]];
imgexp = ExportString[img, "JPEG", "CompressionLevel" -> .85];
GaussianFilter[
 Binarize@ImageResize[ImportString[imgexp, "JPEG"], 
   ImageDimensions[img]*2], 2]

Answer 2

The key word you want in your search is "XKCD". These probably do much of what you want:

https://blog.wolfram.com/2012/10/05/automating-xkcd-diagrams-transforming-serious-to-funny/

xkcd-style Plots

Answer 3

Blurring the image doesn't do it much justice. So, as a better attempt, i convolved using randomly generated matrices (3x3) or (4x4) until something looks hand drawn.

sfx = {s1, s3};

{{{0.398698,-0.364446,-0.641229,-0.911284},
{-0.548265,0.909492,0.498542,0.713565},
{-0.597513,-0.179438,0.16953,0.875084},
{-0.0615662,0.56853,0.449008,0.494057}},

{{-0.899334,0.92734,-0.323124,0.921478},
{0.395261,0.322598,0.984112,0.12986},
{0.87857,-0.432671,-0.543319,-0.52283},
{0.327602,0.805195,-0.669803,-0.192092}}}

g1 can be replaced with any "Graphics".

ImageConvolve[g1, #] & /@ sfx

A bit more careless rendering:

Try:

ImageConvolve[g1,{{-1.4, 0, 0.5}, {0.1, 1, 0.2}, {0.4, 0.4, -0.1}}]

But since you are writing the book on Math, you are more qualified to come up with a suitable kernel. I would put it inside a lengthy manipulate to get just the right look. Over time a catalog of effects will emerge.

Observation: This picture seems to have been put together with a few "cut-paste" paper sections (or perhaps the scanner drive belt was malfunctioning).

Another method could be to do ImagePartition first. ImageAssemble can then put the image sections back with small and random translation/rotation effects; each section being slightly differently manipulated to replicate this retro effect.

Regards