How to design a mountain logo

Question

I want to create mountain logos similar to this one:

I started accumalating random integer sequences looking for a solution with the Filling-option of ListLinePlot. But this went utterly wrong. Maybe, a better way would be to use Graphics with some Polygons arranged in a proper way?

Solutions starting with an Image and using the Image-processing capabilities of Mathematica are also possible. Take f.e this one:

The solution should be simple enough to to serve as a logo (not too many peaks and spikes) and should also provide some random variations, a user could choose from.

Answer 1

Here is an attempt with triangles.

numberOfPeaks = 4;

randomlogos = 
  Table[coords = 
    Table[RandomReal[] {{0 + RandomReal[], 0}, {1 + RandomReal[], 
        1}, {2 + RandomReal[], 0}}, numberOfPeaks];
   coords2 = Table[
     newymax = c[[2, 2]] - RandomReal[{c[[2, 2]]/3, 0}];
     newxmin = (newymax - 
          c[[2, 2]]) ((c[[2, 1]] - c[[1, 1]])/(c[[2, 2]] - 
            c[[1, 2]])) + c[[2, 1]];
     newxmax = (newymax - 
          c[[2, 2]]) ((c[[2, 1]] - c[[3, 1]])/(c[[2, 2]] - 
            c[[3, 2]])) + c[[2, 1]];
     {c[[1]], {RandomReal[{newxmin, newxmax}], 
       RandomReal[{c[[2, 2]]/2, newymax}]}, c[[3]]}, {c, coords}];
   Graphics[{Triangle[coords], White, Triangle[coords2]}]
   , 10];

Column[randomlogos]

Answer 2

I found a way to do this with Adobe Firefly. I think this might get downvoted because it's not using Mathematica. However, maybe you could use ImageSynthesize to do this. Anyways, here's a result. There is a feature request ImageSynthesize and Adobe Firefly if you have access you can visit.

Here's another one with material that I removed but for some reason the material didn't stay removed so I guess you'll have to manually remove it.

The prompt was

a mountain logo with black and white and sharp peaks in vector form with peaks and spikes

Answer 3

A partial answer

id = ImageData[image];

Review each of the color channels

Image[id[[All, All, 3]]] // Binarize

Start playing with Erosion and Dilation

Review of ImageHistogram[image] may be helpful for filtering the selected channel prior to Binarize to, for example, remove the blue sky by changing the "high" blue values to zero.