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What might be a word for the shape with a lot of random projections and recesses? I would like to describe the shape of countries in Europe where countries have interlocking shapes like distorted jigsaw puzzles. Alternatively, what would be an analogy for irregular shape with female and male connections?

The analogies which come to my mind are:

  • irregular jigsaw puzzle
  • inkblot, puddle, blood pool
  • amoeba with its tentacles (pseudopods)
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    I do like fractal. You can also say that the coastlines are *irregular, with peninsulas and fjords." You can say that the borders aren't smooth, straight lines. You can say that the borders have a protuberations and fingers. – aparente001 Jun 18 at 20:47
  • @aparente001 You mean: protuberances. :) Sorry.... – Lambie Jun 18 at 21:16
  • I think you got off on the wrong foot. European country borders are not "interlocking". If they were, so would all others. They are just shaped irregularly. Like most countries in the world. – Lambie Jun 18 at 21:20
  • I used European borders as an example in opposite to North America or Africa borders. In Europe, the borders are have been shaped by swords and gunpowder in opposite to North America or Africa where the borders resulted from signed agreements. – Przemyslaw Remin Jun 19 at 10:50
  • @aparente001 I like your analogy to an island with "peninsulas and fjords." Do you think that English words like "capes and bays" may be more widely understood? – Przemyslaw Remin Jun 19 at 11:37
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Objects or shapes which intentionally connect are generally described as "interlocking".

This jigsaw puzzle has 1,000 interlocking pieces.

Lego bricks are also described this way.

A similar alternative would be interlinking.

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The borders between countries may be fractal in nature.

Mandelbrot coined the term “fractal” to describe shapes (such as country borders) that exhibit self similarity at different levels of magnification.

from Software Estimation in the Fractal Dimension

(A Penrose tile also came to mind. However, these are regular, interlocking, repeated shapes, not like European countries).

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    country borders are not a good example of fractals. – Lambie Jun 18 at 21:14
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    I am very grateful for mentioning Mr. Penrose. – Przemyslaw Remin Jun 19 at 11:43
  • @Lambie, I agree that the U.S. / Canada border and the South Korean / North Korean border follow latitude great circles and are not fractal. However, please take a look at en.wikipedia.org/wiki/List_of_international_border_rivers in the Europe section. You might observe that many European borders are defined by rivers. Some are defined by mountain ranges. These irregular natural phenomena are fractal (see "Software Estimation" quote). Since rival governments used these natural phenomena in determining borders, one can infer that those country borders are fractal. – rajah9 Jun 19 at 12:59
  • Fractals are a system of representation. They are not things in the real. Fractals are used in picture compression, etc. mathigon.org/world/Fractals – Lambie Jun 19 at 13:40
  • I do not agree that borders are fractal. Fractals are structured, not random. They have repetitive patterns like a snowflake. I am looking for a random amoeba-shape which would be smooth after magnifying. – Przemyslaw Remin Jun 19 at 20:19

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