<p>I am using Fournier's midpoint algorithm (recursive subdivision) to construct a landscape of 1025 x 1025 gridpoints, then I am using an advanced version of box counting to find fractal dimension, D. No matter what Hurst exponent I use in Fournier's algorithm, I get D = 2.0. Has anyone checked Fournier's algorithm for fractal dimension? Does it actually produce a fractal?</p>

CC BY-SA 4.0
2021-05-06T02:25:18.950Z
Is "Fournier's midpoint algorithm" the [Diamond-square algorithm](https://en.wikipedia.org/wiki/Diamond-square_algorithm)?
Anderson Green
CC BY-SA 4.0
2021-05-06T07:29:05.180Z
@Anderson Green Yes.
user993563
CC BY-SA 4.0
2021-05-09T19:24:23.547Z
This Wikipedia page sums it up pretty well: https://en.wikipedia.org/wiki/Fractal_dimension#:~:text=In%20mathematics%2C%20more%20specifically%20in,at%20which%20it%20is%20measured.&text=One%20non-trivial%20example%20is,dimension%20of%20a%20Koch%20snowflake.
pmw1234
CC BY-SA 4.0
2021-05-10T20:22:29.933Z
@pmw1234 Thank you for providing this wikipedia page with some basic information about fractal dimension. I am not sure how it is relevant for the question asked but thank you anyway.
user993563
CC BY-SA 4.0
2021-05-11T11:46:58.847Z
"Box Counting" is an overloaded term and your post doesn't give a good context. Perhaps this will help you: https://en.wikipedia.org/wiki/Minkowski–Bouligand_dimension also, when cross posting please link your posts. https://stackexchange.com/search?q=Fournier%27s+midpoint+algorithm
pmw1234
CC BY-SA 4.0
2021-05-11T22:34:37.653Z
@pmw1234 Thank you for this very detailed reply. I did not quite understand from your comment whether you have checked Fournier's algorithm for fractal dimension as I was specifically asking in my question but thank you anyway. And of course special thanks for this another very interesting wikipedia page. I will read it when I have time. I am not sure if you want me to edit it or not, though. Hope you will be able to detail on this. I also thank you for pointing out the cross-posting issue - this is indeed crucial for understanding the question I asked.
user993563
CC BY-SA 4.0
2021-05-11T22:38:38.423Z
@pmw1234 Also, I am very sorry and truly apologize but I did not understand what you mean by "overloaded". Box counting is known to provide an estimate of H which is not very accurate, but still not as inaccurate as would be suggested by the information I supplied in my question. See e.g. the textbook by Peitgen.
user993563
<algorithm>
Fractal dimension of landscape generated with Fournier's midpoint algorithm (recursive subdivision) is 2.0 no matter what. Why?
user993563
# Fractal dimension of landscape generated with Fournier's midpoint algorithm (recursive subdivision) is 2.0 no matter what. Why?

(Asked by: username_0 on 2021-05-05)

I am using Fournier's midpoint algorithm (recursive subdivision) to construct a landscape of 1025 x 1025 gridpoints, then I am using an advanced version of box counting to find fractal dimension, D. No matter what Hurst exponent I use in Fournier's algorithm, I get D = 2.0. Has anyone checked Fournier's algorithm for fractal dimension? Does it actually produce a fractal?

**Tags:** algorithm

> **Comments:**
> **username_1**: Is "Fournier's midpoint algorithm" the [Diamond-square algorithm](https://en.wikipedia.org/wiki/Diamond-square_algorithm)?  
> **username_0**: @username_1 Yes.  
> **username_2**: This Wikipedia page sums it up pretty well: https://en.wikipedia.org/wiki/Fractal_dimension#:~:text=In%20mathematics%2C%20more%20specifically%20in,at%20which%20it%20is%20measured.&text=One%20non-trivial%20example%20is,dimension%20of%20a%20Koch%20snowflake.  
> **username_0**: @username_2 Thank you for providing this wikipedia page with some basic information about fractal dimension. I am not sure how it is relevant for the question asked but thank you anyway.  
> **username_2**: "Box Counting" is an overloaded term and your post doesn't give a good context. Perhaps this will help you: https://en.wikipedia.org/wiki/Minkowski–Bouligand_dimension also, when cross posting please link your posts. https://stackexchange.com/search?q=Fournier%27s+midpoint+algorithm  
> **username_0**: @username_2 Thank you for this very detailed reply. I did not quite understand from your comment whether you have checked Fournier's algorithm for fractal dimension as I was specifically asking in my question but thank you anyway. And of course special thanks for this another very interesting wikipedia page. I will read it when I have time. I am not sure if you want me to edit it or not, though. Hope you will be able to detail on this. I also thank you for pointing out the cross-posting issue - this is indeed crucial for understanding the question I asked.  
> **username_0**: @username_2 Also, I am very sorry and truly apologize but I did not understand what you mean by "overloaded". Box counting is known to provide an estimate of H which is not very accurate, but still not as inaccurate as would be suggested by the information I supplied in my question. See e.g. the textbook by Peitgen.  

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