How to create a fractal tree?

up vote
3
down vote

favorite

I want to create a fractal tree, using translation and rotation. Code below is working for one level, but when I try loop, it is not giving output. Code is given below:

 threshold = 4;
 L = 100;
 While[
 L > threshold,
 line = Line[0, 0, 0, -L];
 Graphics[
 line, 
 Scale[#, 
 2/3, 0, 
 0] & /@ (Rotate[
 Translate[line, 0, L], # Degree, 0, 0] & /@ -30, 
 30)] 
 L = L*0.67;
 ];

asked Sep 2 at 11:20

BiSarfraz

625

1

Related: 154213.
â€“Â Henrik Schumacher
Sep 2 at 12:09

add a commentÂ |Â

up vote
3
down vote

favorite

I want to create a fractal tree, using translation and rotation. Code below is working for one level, but when I try loop, it is not giving output. Code is given below:

 threshold = 4;
 L = 100;
 While[
 L > threshold,
 line = Line[0, 0, 0, -L];
 Graphics[
 line, 
 Scale[#, 
 2/3, 0, 
 0] & /@ (Rotate[
 Translate[line, 0, L], # Degree, 0, 0] & /@ -30, 
 30)] 
 L = L*0.67;
 ];

asked Sep 2 at 11:20

BiSarfraz

625

1

Related: 154213.
â€“Â Henrik Schumacher
Sep 2 at 12:09

add a commentÂ |Â

up vote
3
down vote

favorite

I want to create a fractal tree, using translation and rotation. Code below is working for one level, but when I try loop, it is not giving output. Code is given below:

 threshold = 4;
 L = 100;
 While[
 L > threshold,
 line = Line[0, 0, 0, -L];
 Graphics[
 line, 
 Scale[#, 
 2/3, 0, 
 0] & /@ (Rotate[
 Translate[line, 0, L], # Degree, 0, 0] & /@ -30, 
 30)] 
 L = L*0.67;
 ];

asked Sep 2 at 11:20

BiSarfraz

625

I want to create a fractal tree, using translation and rotation. Code below is working for one level, but when I try loop, it is not giving output. Code is given below:

 threshold = 4;
 L = 100;
 While[
 L > threshold,
 line = Line[0, 0, 0, -L];
 Graphics[
 line, 
 Scale[#, 
 2/3, 0, 
 0] & /@ (Rotate[
 Translate[line, 0, L], # Degree, 0, 0] & /@ -30, 
 30)] 
 L = L*0.67;
 ];

asked Sep 2 at 11:20

BiSarfraz

625

asked Sep 2 at 11:20

BiSarfraz

625

asked Sep 2 at 11:20

BiSarfraz

625

asked Sep 2 at 11:20

BiSarfraz

625

1

Related: 154213.
â€“Â Henrik Schumacher
Sep 2 at 12:09

add a commentÂ |Â

1

Related: 154213.
â€“Â Henrik Schumacher
Sep 2 at 12:09

Related: 154213.
â€“Â Henrik Schumacher
Sep 2 at 12:09

add a commentÂ |Â

3 Answers
3

active

oldest

votes

up vote
5
down vote

accepted

ClearAll[next];

next[x1_, y1_, x2_, y2_] =
 (
 x1, y1, x2, y2 //
 TranslationTransform[x2 - x1, y2 - y1] //
 RotationTransform[# Pi/6, x2, y2] //
 ScalingTransform[2/3 1, 1, x2, y2]
 ) & /@ -1, 1;

list = NestList[Join @@ next /@ # &, N@0, 0, 0, 1, 5];

Graphics[Line /@ list]

enter image description here

edited Sep 3 at 6:25

answered Sep 2 at 12:55

chyanog

6,75921544

Nice, Thank you so very much @chyang.
â€“Â BiSarfraz
Sep 2 at 14:33

@BiSarfraz You are welcome.
â€“Â chyanog
Sep 3 at 6:25

add a commentÂ |Â

up vote
6
down vote

I am not only new in Mathematica, but also new in Maths. I need a very simple approach

(This answer attempts to be a "reference answer" with relevant links.)

This has been discussed extensively in MSE and Mathematica blogs and demonstrations.

MSE:
- How can I improve my code for drawing a tree?
- L-System in Mathematica

Mathematica Journal:
- A New Method of
  Constructing Fractals and
  Other Graphics

Demonstrations:
- Fractal Trees
- Radial FractalTree
- FibonacciTree

Blogs:
- Adventures into the Mathematical Forest of Fractal Trees.
- Fractals at 4am

edited Sep 2 at 15:06

Szabolcs

152k13415896

answered Sep 2 at 14:07

Anton Antonov

21.5k164107

Thank you so much.
â€“Â BiSarfraz
Sep 2 at 14:25

@BiSarfraz You are welcome, good luck!
â€“Â Anton Antonov
Sep 2 at 14:28

add a commentÂ |Â

up vote
3
down vote

The main issue with your code is that it's lacking a way to combine the different levels of the tree. Graphics are not automatically printed, unless they are the final result of a computation.

The following code should get you started:

tree[L_, th_] /; L > th := With[
 line = Line[0, 0, 0, -L],
 
 line,
 Scale[#, 2/3, 0, 0] & /@ (Rotate[Translate[tree[0.67 L, th], 0, L], # Degree, 0, 0] & /@ -30, 30)
 ]
tree[__] := 


tree[100, 10] // Graphics

Mathematica graphics

The key ingredients are:

Recursion of the tree function to combine the different parts. The termination condition is implemented using Condition (/;)

Rotate,Scale,Transform can be arbitrarily nested, allowing for a clean specification of the nested levels

As you can see, the result is not correct yet (the lines are too short), but you should be able to easily fix that.

answered Sep 2 at 13:01

Lukas Lang

5,1531525

Thank you so much for making things easy.
â€“Â BiSarfraz
Sep 2 at 14:28

1

I have fixed it: line, Scale[#, 2/3, 0, 0] & /@ (Rotate[Translate[tree[0.67 L, th], 0, 0.67L], # Degree, 0, 0] & /@ -30, 30)} ]
â€“Â BiSarfraz
Sep 3 at 10:12

add a commentÂ |Â

Your Answer

StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\$","\$"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "387"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: false,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);

);

draft saved

draft discarded

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f181095%2fhow-to-create-a-fractal-tree%23new-answer', 'question_page');

);

Post as a guest

Name

3 Answers
3

active

oldest

votes

3 Answers
3

active

oldest

votes

up vote
5
down vote

accepted

ClearAll[next];

next[x1_, y1_, x2_, y2_] =
 (
 x1, y1, x2, y2 //
 TranslationTransform[x2 - x1, y2 - y1] //
 RotationTransform[# Pi/6, x2, y2] //
 ScalingTransform[2/3 1, 1, x2, y2]
 ) & /@ -1, 1;

list = NestList[Join @@ next /@ # &, N@0, 0, 0, 1, 5];

Graphics[Line /@ list]

enter image description here

edited Sep 3 at 6:25

answered Sep 2 at 12:55

chyanog

6,75921544

Nice, Thank you so very much @chyang.
â€“Â BiSarfraz
Sep 2 at 14:33

@BiSarfraz You are welcome.
â€“Â chyanog
Sep 3 at 6:25

add a commentÂ |Â

up vote
5
down vote

accepted

ClearAll[next];

next[x1_, y1_, x2_, y2_] =
 (
 x1, y1, x2, y2 //
 TranslationTransform[x2 - x1, y2 - y1] //
 RotationTransform[# Pi/6, x2, y2] //
 ScalingTransform[2/3 1, 1, x2, y2]
 ) & /@ -1, 1;

list = NestList[Join @@ next /@ # &, N@0, 0, 0, 1, 5];

Graphics[Line /@ list]

enter image description here

edited Sep 3 at 6:25

answered Sep 2 at 12:55

chyanog

6,75921544

Nice, Thank you so very much @chyang.
â€“Â BiSarfraz
Sep 2 at 14:33

@BiSarfraz You are welcome.
â€“Â chyanog
Sep 3 at 6:25

add a commentÂ |Â

up vote
5
down vote

accepted

ClearAll[next];

next[x1_, y1_, x2_, y2_] =
 (
 x1, y1, x2, y2 //
 TranslationTransform[x2 - x1, y2 - y1] //
 RotationTransform[# Pi/6, x2, y2] //
 ScalingTransform[2/3 1, 1, x2, y2]
 ) & /@ -1, 1;

list = NestList[Join @@ next /@ # &, N@0, 0, 0, 1, 5];

Graphics[Line /@ list]

enter image description here

edited Sep 3 at 6:25

answered Sep 2 at 12:55

chyanog

6,75921544

ClearAll[next];

next[x1_, y1_, x2_, y2_] =
 (
 x1, y1, x2, y2 //
 TranslationTransform[x2 - x1, y2 - y1] //
 RotationTransform[# Pi/6, x2, y2] //
 ScalingTransform[2/3 1, 1, x2, y2]
 ) & /@ -1, 1;

list = NestList[Join @@ next /@ # &, N@0, 0, 0, 1, 5];

Graphics[Line /@ list]

enter image description here

edited Sep 3 at 6:25

answered Sep 2 at 12:55

chyanog

6,75921544

edited Sep 3 at 6:25

answered Sep 2 at 12:55

chyanog

6,75921544

answered Sep 2 at 12:55

chyanog

6,75921544

answered Sep 2 at 12:55

chyanog

6,75921544

Nice, Thank you so very much @chyang.
â€“Â BiSarfraz
Sep 2 at 14:33

@BiSarfraz You are welcome.
â€“Â chyanog
Sep 3 at 6:25

add a commentÂ |Â

Nice, Thank you so very much @chyang.
â€“Â BiSarfraz
Sep 2 at 14:33

@BiSarfraz You are welcome.
â€“Â chyanog
Sep 3 at 6:25

Nice, Thank you so very much @chyang.
â€“Â BiSarfraz
Sep 2 at 14:33

@BiSarfraz You are welcome.
â€“Â chyanog
Sep 3 at 6:25

add a commentÂ |Â

up vote
6
down vote

I am not only new in Mathematica, but also new in Maths. I need a very simple approach

(This answer attempts to be a "reference answer" with relevant links.)

This has been discussed extensively in MSE and Mathematica blogs and demonstrations.

MSE:
- How can I improve my code for drawing a tree?
- L-System in Mathematica

Mathematica Journal:
- A New Method of
  Constructing Fractals and
  Other Graphics

Demonstrations:
- Fractal Trees
- Radial FractalTree
- FibonacciTree

Blogs:
- Adventures into the Mathematical Forest of Fractal Trees.
- Fractals at 4am

edited Sep 2 at 15:06

Szabolcs

152k13415896

answered Sep 2 at 14:07

Anton Antonov

21.5k164107

Thank you so much.
â€“Â BiSarfraz
Sep 2 at 14:25

@BiSarfraz You are welcome, good luck!
â€“Â Anton Antonov
Sep 2 at 14:28

add a commentÂ |Â

up vote
6
down vote

I am not only new in Mathematica, but also new in Maths. I need a very simple approach

(This answer attempts to be a "reference answer" with relevant links.)

This has been discussed extensively in MSE and Mathematica blogs and demonstrations.

MSE:
- How can I improve my code for drawing a tree?
- L-System in Mathematica

Mathematica Journal:
- A New Method of
  Constructing Fractals and
  Other Graphics

Demonstrations:
- Fractal Trees
- Radial FractalTree
- FibonacciTree

Blogs:
- Adventures into the Mathematical Forest of Fractal Trees.
- Fractals at 4am

edited Sep 2 at 15:06

Szabolcs

152k13415896

answered Sep 2 at 14:07

Anton Antonov

21.5k164107

Thank you so much.
â€“Â BiSarfraz
Sep 2 at 14:25

@BiSarfraz You are welcome, good luck!
â€“Â Anton Antonov
Sep 2 at 14:28

add a commentÂ |Â

up vote
6
down vote

I am not only new in Mathematica, but also new in Maths. I need a very simple approach

(This answer attempts to be a "reference answer" with relevant links.)

This has been discussed extensively in MSE and Mathematica blogs and demonstrations.

MSE:
- How can I improve my code for drawing a tree?
- L-System in Mathematica

Mathematica Journal:
- A New Method of
  Constructing Fractals and
  Other Graphics

Demonstrations:
- Fractal Trees
- Radial FractalTree
- FibonacciTree

Blogs:
- Adventures into the Mathematical Forest of Fractal Trees.
- Fractals at 4am

edited Sep 2 at 15:06

Szabolcs

152k13415896

answered Sep 2 at 14:07

Anton Antonov

21.5k164107

I am not only new in Mathematica, but also new in Maths. I need a very simple approach

(This answer attempts to be a "reference answer" with relevant links.)

This has been discussed extensively in MSE and Mathematica blogs and demonstrations.

MSE:
- How can I improve my code for drawing a tree?
- L-System in Mathematica

Mathematica Journal:
- A New Method of
  Constructing Fractals and
  Other Graphics

Demonstrations:
- Fractal Trees
- Radial FractalTree
- FibonacciTree

Blogs:
- Adventures into the Mathematical Forest of Fractal Trees.
- Fractals at 4am

edited Sep 2 at 15:06

Szabolcs

152k13415896

answered Sep 2 at 14:07

Anton Antonov

21.5k164107

edited Sep 2 at 15:06

Szabolcs

152k13415896

edited Sep 2 at 15:06

Szabolcs

152k13415896

edited Sep 2 at 15:06

Szabolcs

152k13415896

answered Sep 2 at 14:07

Anton Antonov

21.5k164107

answered Sep 2 at 14:07

Anton Antonov

21.5k164107

answered Sep 2 at 14:07

Anton Antonov

21.5k164107

Thank you so much.
â€“Â BiSarfraz
Sep 2 at 14:25

@BiSarfraz You are welcome, good luck!
â€“Â Anton Antonov
Sep 2 at 14:28

add a commentÂ |Â

Thank you so much.
â€“Â BiSarfraz
Sep 2 at 14:25

@BiSarfraz You are welcome, good luck!
â€“Â Anton Antonov
Sep 2 at 14:28

Thank you so much.
â€“Â BiSarfraz
Sep 2 at 14:25

@BiSarfraz You are welcome, good luck!
â€“Â Anton Antonov
Sep 2 at 14:28

add a commentÂ |Â

up vote
3
down vote

The main issue with your code is that it's lacking a way to combine the different levels of the tree. Graphics are not automatically printed, unless they are the final result of a computation.

The following code should get you started:

tree[L_, th_] /; L > th := With[
 line = Line[0, 0, 0, -L],
 
 line,
 Scale[#, 2/3, 0, 0] & /@ (Rotate[Translate[tree[0.67 L, th], 0, L], # Degree, 0, 0] & /@ -30, 30)
 ]
tree[__] := 


tree[100, 10] // Graphics

Mathematica graphics

The key ingredients are:

Recursion of the tree function to combine the different parts. The termination condition is implemented using Condition (/;)

Rotate,Scale,Transform can be arbitrarily nested, allowing for a clean specification of the nested levels

As you can see, the result is not correct yet (the lines are too short), but you should be able to easily fix that.

answered Sep 2 at 13:01

Lukas Lang

5,1531525

Thank you so much for making things easy.
â€“Â BiSarfraz
Sep 2 at 14:28

1

I have fixed it: line, Scale[#, 2/3, 0, 0] & /@ (Rotate[Translate[tree[0.67 L, th], 0, 0.67L], # Degree, 0, 0] & /@ -30, 30)} ]
â€“Â BiSarfraz
Sep 3 at 10:12

add a commentÂ |Â

up vote
3
down vote

The main issue with your code is that it's lacking a way to combine the different levels of the tree. Graphics are not automatically printed, unless they are the final result of a computation.

The following code should get you started:

tree[L_, th_] /; L > th := With[
 line = Line[0, 0, 0, -L],
 
 line,
 Scale[#, 2/3, 0, 0] & /@ (Rotate[Translate[tree[0.67 L, th], 0, L], # Degree, 0, 0] & /@ -30, 30)
 ]
tree[__] := 


tree[100, 10] // Graphics

Mathematica graphics

The key ingredients are:

Recursion of the tree function to combine the different parts. The termination condition is implemented using Condition (/;)

Rotate,Scale,Transform can be arbitrarily nested, allowing for a clean specification of the nested levels

As you can see, the result is not correct yet (the lines are too short), but you should be able to easily fix that.

answered Sep 2 at 13:01

Lukas Lang

5,1531525

Thank you so much for making things easy.
â€“Â BiSarfraz
Sep 2 at 14:28

1

I have fixed it: line, Scale[#, 2/3, 0, 0] & /@ (Rotate[Translate[tree[0.67 L, th], 0, 0.67L], # Degree, 0, 0] & /@ -30, 30)} ]
â€“Â BiSarfraz
Sep 3 at 10:12

add a commentÂ |Â

up vote
3
down vote

The main issue with your code is that it's lacking a way to combine the different levels of the tree. Graphics are not automatically printed, unless they are the final result of a computation.

The following code should get you started:

tree[L_, th_] /; L > th := With[
 line = Line[0, 0, 0, -L],
 
 line,
 Scale[#, 2/3, 0, 0] & /@ (Rotate[Translate[tree[0.67 L, th], 0, L], # Degree, 0, 0] & /@ -30, 30)
 ]
tree[__] := 


tree[100, 10] // Graphics

Mathematica graphics

The key ingredients are:

Recursion of the tree function to combine the different parts. The termination condition is implemented using Condition (/;)

Rotate,Scale,Transform can be arbitrarily nested, allowing for a clean specification of the nested levels

As you can see, the result is not correct yet (the lines are too short), but you should be able to easily fix that.

answered Sep 2 at 13:01

Lukas Lang

5,1531525

The main issue with your code is that it's lacking a way to combine the different levels of the tree. Graphics are not automatically printed, unless they are the final result of a computation.

The following code should get you started:

tree[L_, th_] /; L > th := With[
 line = Line[0, 0, 0, -L],
 
 line,
 Scale[#, 2/3, 0, 0] & /@ (Rotate[Translate[tree[0.67 L, th], 0, L], # Degree, 0, 0] & /@ -30, 30)
 ]
tree[__] := 


tree[100, 10] // Graphics

Mathematica graphics

The key ingredients are:

Recursion of the tree function to combine the different parts. The termination condition is implemented using Condition (/;)

Rotate,Scale,Transform can be arbitrarily nested, allowing for a clean specification of the nested levels

As you can see, the result is not correct yet (the lines are too short), but you should be able to easily fix that.

answered Sep 2 at 13:01

Lukas Lang

5,1531525

answered Sep 2 at 13:01

Lukas Lang

5,1531525

answered Sep 2 at 13:01

Lukas Lang

5,1531525

answered Sep 2 at 13:01

Lukas Lang

5,1531525

Thank you so much for making things easy.
â€“Â BiSarfraz
Sep 2 at 14:28

1

I have fixed it: line, Scale[#, 2/3, 0, 0] & /@ (Rotate[Translate[tree[0.67 L, th], 0, 0.67L], # Degree, 0, 0] & /@ -30, 30)} ]
â€“Â BiSarfraz
Sep 3 at 10:12

add a commentÂ |Â

Thank you so much for making things easy.
â€“Â BiSarfraz
Sep 2 at 14:28

1

I have fixed it: line, Scale[#, 2/3, 0, 0] & /@ (Rotate[Translate[tree[0.67 L, th], 0, 0.67L], # Degree, 0, 0] & /@ -30, 30)} ]
â€“Â BiSarfraz
Sep 3 at 10:12

Thank you so much for making things easy.
â€“Â BiSarfraz
Sep 2 at 14:28

I have fixed it: line, Scale[#, 2/3, 0, 0] & /@ (Rotate[Translate[tree[0.67 L, th], 0, 0.67L], # Degree, 0, 0] & /@ -30, 30)} ]
â€“Â BiSarfraz
Sep 3 at 10:12

add a commentÂ |Â

draft saved

draft discarded

draft saved

draft discarded

Post as a guest

Name

Search This Blog

Iyfjky