###### Descriptions and Examples for the POV-Ray Raytracerby Friedrich A. Lohmüller About Loops with POV-Ray
Italiano
Français
Deutsch

Home
- POV-Ray Tutorial

Loops in POV-Ray
1. Loops For + While
Comparison
2. Linear
Transformations
3. Circular
Transformations
4. Moebius etc.
5. Screws
& Spirals
6. Twisting
Spirals
7. Snails
& Ammonites
8. Spherical Spirals 1
9. Spherical Spirals 2
>10. Fibonacci Spirals

## Spirals by Fibonacci Numbers

Here we use the proportion between two Fibonacci numbers
to calculate the rotation angle of the spiral elements.
 ```#local R = 0.25; // start radius #local Nr = 0; // start #local End_Nr = 37; // end #while ( Nr <= End_Nr ) // loop sphere{ <0,0,0>, R*0.25 //------------ scale <1,0.6,1> texture{ pigment{color rgb<0.8,1,0>} finish {phong 1} } //-------------- translate rotate <0,-Nr*360*(8/13),0> } //----------------------------- #local R = R*1.05; // growing radius #local Nr = Nr + 1; // next Nr #end // --------------- end of loop```
The same precedure with a for-loop:
 ```#local R = 0.25; // start radius //#for(Identifier,Start,End[,Step]) #for ( Nr , 0, 37, 1 ) sphere{ <0,0,0>, R*0.25 //------------ scale <1,0.6,1> texture{ pigment{color rgb<0.8,1,0>} finish {phong 1} } //-------------- translate rotate <0,-Nr*360*(8/13),0> } //----------------------------- #local R = R*1.05; // growing radius #end // --------------- end of loop```
// Fibonacci numbers:
// Rules: A(1)= 1; A(2) = 1; and
//            for N>2: A(N) = A(N-1) + A(N-2).
// 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ...

Scene file for POV-Ray: FibonacciSpiral_01.pov
or: FibonacciSpiral_01.txt

With a linear growing of the radius R
we get the following form:
 ```#local R = 0.018; // start radius #local Nr = 0; // start #local End_Nr = 300; // end #while ( Nr <= End_Nr ) // loop sphere{ <0,0,0>,0.25 + Nr*0.0015 //---- scale <1,1.6,1> texture{ pigment{color rgb<1,0.7,0>} finish {phong 1} } //-------------- translate rotate <0,-Nr*360*(34/89),0> } //----------------------------- #local R = R+0.038; // growing radius #local Nr = Nr + 1; // next Nr #end // --------------- end of loop```
Scene file for POV-Ray: FibonacciSpiral_05.pov
or: FibonacciSpiral_05.txt

 Overview | For + While | Linear | Circular | Moebius | Screws+Spirals | Twisted Spirals | Snails | Spherical 1 | Spherical 2 | Fibonacci |
top

 © Friedrich A. Lohmüller, 2014 http://www.f-lohmueller.de