Drawing many random paths in TikZ

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I'm trying to draw a diagram in TikZ that helps visually explain an analogy I'm trying to make in a paper. Basically, I want to start with a plane that contains many random paths of different lengths, such as that below. I created that diagram by compiling the code below in LuaLaTeX, which combines two other answers on the site (at Drawing random paths and Drawing in random locations -- you will need to use the poisson disc sampling library the latter refers to).

I want to make a few tweaks to the output. Firstly, to tidy it up, I don't want the paths to be able to turn back on themselves so easily, so as to eliminate the sharp kinks and arrowheads pointing the 'wrong' direction in some of the paths. Secondly, if possible, I want some of the paths to be loosely correlated to one another: as if certain paths had a mass that gravitationally attracted the paths around them to some degree. And I want these certain paths to be drawn in a different colour to all the other paths.

Is this possible? I'd be very grateful for any help.

RequirePackageluatex85
documentclassstandalone
usepackagetikz
usepackagepoisson
begindocument
edefmylistpoissonpointslist1050.3320

begintikzpicture

foreach x/y in mylist 
 draw[->, rounded corners=5pt] (x,y)
 foreach i in 1,...,3 
 -- ++(rnd*180:rnd)
 ;


endtikzpicture
enddocument

tikz-pgf luatex diagrams random randomwalk

share|improve this question

asked 59 mins ago

solisoc

615

add a comment | 

up vote
2
down vote

favorite

I'm trying to draw a diagram in TikZ that helps visually explain an analogy I'm trying to make in a paper. Basically, I want to start with a plane that contains many random paths of different lengths, such as that below. I created that diagram by compiling the code below in LuaLaTeX, which combines two other answers on the site (at Drawing random paths and Drawing in random locations -- you will need to use the poisson disc sampling library the latter refers to).

I want to make a few tweaks to the output. Firstly, to tidy it up, I don't want the paths to be able to turn back on themselves so easily, so as to eliminate the sharp kinks and arrowheads pointing the 'wrong' direction in some of the paths. Secondly, if possible, I want some of the paths to be loosely correlated to one another: as if certain paths had a mass that gravitationally attracted the paths around them to some degree. And I want these certain paths to be drawn in a different colour to all the other paths.

Is this possible? I'd be very grateful for any help.

RequirePackageluatex85
documentclassstandalone
usepackagetikz
usepackagepoisson
begindocument
edefmylistpoissonpointslist1050.3320

begintikzpicture

foreach x/y in mylist 
 draw[->, rounded corners=5pt] (x,y)
 foreach i in 1,...,3 
 -- ++(rnd*180:rnd)
 ;


endtikzpicture
enddocument

tikz-pgf luatex diagrams random randomwalk

share|improve this question

asked 59 mins ago

solisoc

615

add a comment | 

up vote
2
down vote

favorite

up vote
2
down vote

favorite

I'm trying to draw a diagram in TikZ that helps visually explain an analogy I'm trying to make in a paper. Basically, I want to start with a plane that contains many random paths of different lengths, such as that below. I created that diagram by compiling the code below in LuaLaTeX, which combines two other answers on the site (at Drawing random paths and Drawing in random locations -- you will need to use the poisson disc sampling library the latter refers to).

I want to make a few tweaks to the output. Firstly, to tidy it up, I don't want the paths to be able to turn back on themselves so easily, so as to eliminate the sharp kinks and arrowheads pointing the 'wrong' direction in some of the paths. Secondly, if possible, I want some of the paths to be loosely correlated to one another: as if certain paths had a mass that gravitationally attracted the paths around them to some degree. And I want these certain paths to be drawn in a different colour to all the other paths.

Is this possible? I'd be very grateful for any help.

RequirePackageluatex85
documentclassstandalone
usepackagetikz
usepackagepoisson
begindocument
edefmylistpoissonpointslist1050.3320

begintikzpicture

foreach x/y in mylist 
 draw[->, rounded corners=5pt] (x,y)
 foreach i in 1,...,3 
 -- ++(rnd*180:rnd)
 ;


endtikzpicture
enddocument

tikz-pgf luatex diagrams random randomwalk

share|improve this question

asked 59 mins ago

solisoc

615

I'm trying to draw a diagram in TikZ that helps visually explain an analogy I'm trying to make in a paper. Basically, I want to start with a plane that contains many random paths of different lengths, such as that below. I created that diagram by compiling the code below in LuaLaTeX, which combines two other answers on the site (at Drawing random paths and Drawing in random locations -- you will need to use the poisson disc sampling library the latter refers to).

I want to make a few tweaks to the output. Firstly, to tidy it up, I don't want the paths to be able to turn back on themselves so easily, so as to eliminate the sharp kinks and arrowheads pointing the 'wrong' direction in some of the paths. Secondly, if possible, I want some of the paths to be loosely correlated to one another: as if certain paths had a mass that gravitationally attracted the paths around them to some degree. And I want these certain paths to be drawn in a different colour to all the other paths.

Is this possible? I'd be very grateful for any help.

RequirePackageluatex85
documentclassstandalone
usepackagetikz
usepackagepoisson
begindocument
edefmylistpoissonpointslist1050.3320

begintikzpicture

foreach x/y in mylist 
 draw[->, rounded corners=5pt] (x,y)
 foreach i in 1,...,3 
 -- ++(rnd*180:rnd)
 ;


endtikzpicture
enddocument

tikz-pgf luatex diagrams random randomwalk

tikz-pgf luatex diagrams random randomwalk

share|improve this question

asked 59 mins ago

solisoc

615

share|improve this question

asked 59 mins ago

solisoc

615

share|improve this question

share|improve this question

asked 59 mins ago

solisoc

615

asked 59 mins ago

solisoc

615

asked 59 mins ago

solisoc

615

615

add a comment | 

add a comment | 

1 Answer
1

active

oldest

votes

up vote
3
down vote

Something like this?

RequirePackageluatex85
documentclassstandalone
usepackagetikz
usepackagepoisson
begindocument
edefmylistpoissonpointslist1050.3320

begintikzpicture

foreach x/y in mylist 
 pgfmathsetmacromyrndrnd*360
 pgfmathsetmacromydistpow(x*x+y*y,1/3)/4
 draw[->, rounded corners=5pt] (mydist*x,mydist*y)
 foreach i in 1,...,3 
 -- ++(myrnd+rnd*60:rnd)
 ;

endtikzpicture
enddocument

I first compute a main angle and then add fluctuations to it which are between -60 and +60. To make the objects cluster, I add a function that will move things that are close to the clustering point a bit closer to it, and things that are remote even a bit further away.

Here is another proposal in which the directions are correlated, and the sharp corners are gone. They appear above because some segments are super short.

RequirePackageluatex85
documentclassstandalone
usepackagetikz
usepackagepoisson
begindocument
edefmylistpoissonpointslist1050.3320

begintikzpicture
foreach x/y in mylist 
 pgfmathsetmacromyrndrnd*60+(x+y)*120
 pgfmathsetmacromydistpow(x*x+y*y,1/3)/4
 draw[->, rounded corners=10pt] (mydist*x,mydist*y)
 foreach i in 1,...,3 
 -- ++(myrnd+rnd*60:0.2+0.8*rnd)
 ;

endtikzpicture
enddocument

share|improve this answer

edited 12 mins ago

answered 45 mins ago

marmot

71.9k477153

• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is an intriguing approach, thanks. However, I can still see lines with sharp, abrupt kinks in your output. And while you do produce a nice cluster, the behaviour I'm looking for is not so much lines getting closer together as lines nearby a certain line resembling that certain line more (roughly). I may have been unclear about this in the question.
  – solisoc
  22 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @solisoc I added another option.
  – marmot
  12 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is very close to the desired output. However, I can still spot kinked lines in your output: I've circled two examples at the link below. Is there any way to eradicate them entirely? i.stack.imgur.com/HTbmo.jpg
  – solisoc
  4 mins ago
  

  
  
  
  

add a comment | 

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
3
down vote

Something like this?

RequirePackageluatex85
documentclassstandalone
usepackagetikz
usepackagepoisson
begindocument
edefmylistpoissonpointslist1050.3320

begintikzpicture

foreach x/y in mylist 
 pgfmathsetmacromyrndrnd*360
 pgfmathsetmacromydistpow(x*x+y*y,1/3)/4
 draw[->, rounded corners=5pt] (mydist*x,mydist*y)
 foreach i in 1,...,3 
 -- ++(myrnd+rnd*60:rnd)
 ;

endtikzpicture
enddocument

I first compute a main angle and then add fluctuations to it which are between -60 and +60. To make the objects cluster, I add a function that will move things that are close to the clustering point a bit closer to it, and things that are remote even a bit further away.

Here is another proposal in which the directions are correlated, and the sharp corners are gone. They appear above because some segments are super short.

RequirePackageluatex85
documentclassstandalone
usepackagetikz
usepackagepoisson
begindocument
edefmylistpoissonpointslist1050.3320

begintikzpicture
foreach x/y in mylist 
 pgfmathsetmacromyrndrnd*60+(x+y)*120
 pgfmathsetmacromydistpow(x*x+y*y,1/3)/4
 draw[->, rounded corners=10pt] (mydist*x,mydist*y)
 foreach i in 1,...,3 
 -- ++(myrnd+rnd*60:0.2+0.8*rnd)
 ;

endtikzpicture
enddocument

share|improve this answer

edited 12 mins ago

answered 45 mins ago

marmot

71.9k477153

• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is an intriguing approach, thanks. However, I can still see lines with sharp, abrupt kinks in your output. And while you do produce a nice cluster, the behaviour I'm looking for is not so much lines getting closer together as lines nearby a certain line resembling that certain line more (roughly). I may have been unclear about this in the question.
  – solisoc
  22 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @solisoc I added another option.
  – marmot
  12 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is very close to the desired output. However, I can still spot kinked lines in your output: I've circled two examples at the link below. Is there any way to eradicate them entirely? i.stack.imgur.com/HTbmo.jpg
  – solisoc
  4 mins ago
  

  
  
  
  

add a comment | 

up vote
3
down vote

Something like this?

RequirePackageluatex85
documentclassstandalone
usepackagetikz
usepackagepoisson
begindocument
edefmylistpoissonpointslist1050.3320

begintikzpicture

foreach x/y in mylist 
 pgfmathsetmacromyrndrnd*360
 pgfmathsetmacromydistpow(x*x+y*y,1/3)/4
 draw[->, rounded corners=5pt] (mydist*x,mydist*y)
 foreach i in 1,...,3 
 -- ++(myrnd+rnd*60:rnd)
 ;

endtikzpicture
enddocument

I first compute a main angle and then add fluctuations to it which are between -60 and +60. To make the objects cluster, I add a function that will move things that are close to the clustering point a bit closer to it, and things that are remote even a bit further away.

Here is another proposal in which the directions are correlated, and the sharp corners are gone. They appear above because some segments are super short.

RequirePackageluatex85
documentclassstandalone
usepackagetikz
usepackagepoisson
begindocument
edefmylistpoissonpointslist1050.3320

begintikzpicture
foreach x/y in mylist 
 pgfmathsetmacromyrndrnd*60+(x+y)*120
 pgfmathsetmacromydistpow(x*x+y*y,1/3)/4
 draw[->, rounded corners=10pt] (mydist*x,mydist*y)
 foreach i in 1,...,3 
 -- ++(myrnd+rnd*60:0.2+0.8*rnd)
 ;

endtikzpicture
enddocument

share|improve this answer

edited 12 mins ago

answered 45 mins ago

marmot

71.9k477153

• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is an intriguing approach, thanks. However, I can still see lines with sharp, abrupt kinks in your output. And while you do produce a nice cluster, the behaviour I'm looking for is not so much lines getting closer together as lines nearby a certain line resembling that certain line more (roughly). I may have been unclear about this in the question.
  – solisoc
  22 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @solisoc I added another option.
  – marmot
  12 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is very close to the desired output. However, I can still spot kinked lines in your output: I've circled two examples at the link below. Is there any way to eradicate them entirely? i.stack.imgur.com/HTbmo.jpg
  – solisoc
  4 mins ago
  

  
  
  
  

add a comment | 

up vote
3
down vote

up vote
3
down vote

Something like this?

RequirePackageluatex85
documentclassstandalone
usepackagetikz
usepackagepoisson
begindocument
edefmylistpoissonpointslist1050.3320

begintikzpicture

foreach x/y in mylist 
 pgfmathsetmacromyrndrnd*360
 pgfmathsetmacromydistpow(x*x+y*y,1/3)/4
 draw[->, rounded corners=5pt] (mydist*x,mydist*y)
 foreach i in 1,...,3 
 -- ++(myrnd+rnd*60:rnd)
 ;

endtikzpicture
enddocument

I first compute a main angle and then add fluctuations to it which are between -60 and +60. To make the objects cluster, I add a function that will move things that are close to the clustering point a bit closer to it, and things that are remote even a bit further away.

Here is another proposal in which the directions are correlated, and the sharp corners are gone. They appear above because some segments are super short.

RequirePackageluatex85
documentclassstandalone
usepackagetikz
usepackagepoisson
begindocument
edefmylistpoissonpointslist1050.3320

begintikzpicture
foreach x/y in mylist 
 pgfmathsetmacromyrndrnd*60+(x+y)*120
 pgfmathsetmacromydistpow(x*x+y*y,1/3)/4
 draw[->, rounded corners=10pt] (mydist*x,mydist*y)
 foreach i in 1,...,3 
 -- ++(myrnd+rnd*60:0.2+0.8*rnd)
 ;

endtikzpicture
enddocument

share|improve this answer

edited 12 mins ago

answered 45 mins ago

marmot

71.9k477153

Something like this?

RequirePackageluatex85
documentclassstandalone
usepackagetikz
usepackagepoisson
begindocument
edefmylistpoissonpointslist1050.3320

begintikzpicture

foreach x/y in mylist 
 pgfmathsetmacromyrndrnd*360
 pgfmathsetmacromydistpow(x*x+y*y,1/3)/4
 draw[->, rounded corners=5pt] (mydist*x,mydist*y)
 foreach i in 1,...,3 
 -- ++(myrnd+rnd*60:rnd)
 ;

endtikzpicture
enddocument

I first compute a main angle and then add fluctuations to it which are between -60 and +60. To make the objects cluster, I add a function that will move things that are close to the clustering point a bit closer to it, and things that are remote even a bit further away.

Here is another proposal in which the directions are correlated, and the sharp corners are gone. They appear above because some segments are super short.

RequirePackageluatex85
documentclassstandalone
usepackagetikz
usepackagepoisson
begindocument
edefmylistpoissonpointslist1050.3320

begintikzpicture
foreach x/y in mylist 
 pgfmathsetmacromyrndrnd*60+(x+y)*120
 pgfmathsetmacromydistpow(x*x+y*y,1/3)/4
 draw[->, rounded corners=10pt] (mydist*x,mydist*y)
 foreach i in 1,...,3 
 -- ++(myrnd+rnd*60:0.2+0.8*rnd)
 ;

endtikzpicture
enddocument

share|improve this answer

edited 12 mins ago

answered 45 mins ago

marmot

71.9k477153

share|improve this answer

share|improve this answer

edited 12 mins ago

edited 12 mins ago

edited 12 mins ago

answered 45 mins ago

marmot

71.9k477153

answered 45 mins ago

marmot

71.9k477153

answered 45 mins ago

marmot

71.9k477153

71.9k477153

• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is an intriguing approach, thanks. However, I can still see lines with sharp, abrupt kinks in your output. And while you do produce a nice cluster, the behaviour I'm looking for is not so much lines getting closer together as lines nearby a certain line resembling that certain line more (roughly). I may have been unclear about this in the question.
  – solisoc
  22 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @solisoc I added another option.
  – marmot
  12 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is very close to the desired output. However, I can still spot kinked lines in your output: I've circled two examples at the link below. Is there any way to eradicate them entirely? i.stack.imgur.com/HTbmo.jpg
  – solisoc
  4 mins ago
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is an intriguing approach, thanks. However, I can still see lines with sharp, abrupt kinks in your output. And while you do produce a nice cluster, the behaviour I'm looking for is not so much lines getting closer together as lines nearby a certain line resembling that certain line more (roughly). I may have been unclear about this in the question.
  – solisoc
  22 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @solisoc I added another option.
  – marmot
  12 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is very close to the desired output. However, I can still spot kinked lines in your output: I've circled two examples at the link below. Is there any way to eradicate them entirely? i.stack.imgur.com/HTbmo.jpg
  – solisoc
  4 mins ago
  

  
  
  
  

This is an intriguing approach, thanks. However, I can still see lines with sharp, abrupt kinks in your output. And while you do produce a nice cluster, the behaviour I'm looking for is not so much lines getting closer together as lines nearby a certain line resembling that certain line more (roughly). I may have been unclear about this in the question.
– solisoc
22 mins ago

This is an intriguing approach, thanks. However, I can still see lines with sharp, abrupt kinks in your output. And while you do produce a nice cluster, the behaviour I'm looking for is not so much lines getting closer together as lines nearby a certain line resembling that certain line more (roughly). I may have been unclear about this in the question.
– solisoc
22 mins ago

@solisoc I added another option.
– marmot
12 mins ago

@solisoc I added another option.
– marmot
12 mins ago

This is very close to the desired output. However, I can still spot kinked lines in your output: I've circled two examples at the link below. Is there any way to eradicate them entirely? i.stack.imgur.com/HTbmo.jpg
– solisoc
4 mins ago

This is very close to the desired output. However, I can still spot kinked lines in your output: I've circled two examples at the link below. Is there any way to eradicate them entirely? i.stack.imgur.com/HTbmo.jpg
– solisoc
4 mins ago

add a comment | 

 

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