Hans Walser, [20150821]
Visualizations of the Fibonacci recursion
Figure 1 depicts a classical visualization.
Fig. 1: Classical
We have a spiral arrangement without overlapping squares.
In this figure and also in the following we use a color code according to table 1.
No 
RGB 
Color 
Example 
New No 
Fibonacci 
0 
0,0,0 
Black 

1 
1 
1 
0,0,1 
Blue 

2 
1 
2 
0,1,0 
Green 

3 
2 
3 
0,1,1 
Cyan 

4 
3 
4 
1,0,0 
Red 

5 
5 
5 
1,0,1 
Magenta 

6 
8 
6 
1,1,0 
Yellow 

7 
13 
7 
1,1,1 
White 

8 
21 
Tab. 1: Color code
In figure 2 we have a linear arrangement.
Fig. 2: Linear arrangement
This can be done also with other polygons. The figure 3 gives a version with regular triangles.
Fig. 3: Regular triangles
The figure 4 works with regular pentagons.
Fig. 4: Regular pentagons
The ŇrooflineÓ is not straightforward, but interrupted.
Taking a geometric sequence based on the golden section
leads to a proper roofline (Fig. 5). But this is no more a Fibonacci sequence. The difference is visible at the beginning.
Fig. 5: Golden section
Parts of this figure can be used to draw a regular pentagon (Fig. 6).
Fig. 6: Pentagon
In the following figures we will work again with the Fibonacci sequence.
The figure 7 uses half hexagons.
Fig. 7: Half hexagons
In figure 8 half circles.
Fig. 8: Half circles
In figure 9 half circles again, but this time with a golden geometric sequence.
Fig. 9: Golden section