Chapter 9 Designs using Fibonnacci Sequence

This chapter shows designs using papers made in Chapter 5, as finished designs or photographs of stages or alternative designs, of the: 

Fibonnacci Sequence
Golden Section

Both are found in nature and are useful for producing balance in patterns for fabric pieces, using the sequence 0,1,1,2,3,5,8,13,21,34 and so on, where the next in the sequence is made up by adding the previous two numbers

Firstly, diagrams (not shown) using 1 cm units were drawn up on graph paper.
Then the following exercises were carried out:
All designs are labelled F1(Fibonnacci) or GS 1(Golden Section) and so on.
They are in 1cm units using 1,2,3,5,8 unless otherwise stated

Fibonnacci Sequence

F1. Five patterned papers graded into a gradual tonal column

  

F2. The above, divided at right angles into the Fibonacci sequence and stuck onto paper with spaces between each section

F3. More strips from the same sequence of papers arranged in a different way

(The original piece contains two more strips to the left 1cm and 8cm following the alternating sequence as the others, folded over to fit the A4 scan)

F4. One patterned and one plain paper were cut into the Fibonnacci sequence, arranged alternately and glued down

F5. The above design was then cut and arranged on plain background leaving gaps based on the Fibonnacci sequence

F6. Using the same pieces as the above the design was then rearranged as alternating pieces some up some down with no spacing and stuck down

(The original piece contains two more strips to the right 1cm and 8cm following the alternating sequence as the others, folded over to fit the A4 scan)

F7. This shows a new block of five papers, where a second is produced and laid next to and on top of each other, one the reverse of the other

F8a. and F8b. Show different examples of using one block of the above design cut into equal strip widths (2cm) and forming two different fractured designs
F8a is more fractured than F8b

F9. The same strips as in F8a. were used to make a square design based on the 'Log Cabin method' starting with two parallel strips then placing the next strip at right angles and continuing in a clockwise direction with the other strips

This was then stuck down on to a plain background.
It was fascinating how the pattern evolved, highlighted by the curly pattern, presenting a different balanced arrangement from those in Chapter 7

F10a to F10i  These designs evolved from a new block
The block was initially cut into two triangles with 45 degree angles
See F10a,b,c 
Then cut into diagonal (45degree) strips.  All but F10d use the whole square.
F10i I particularly like and can see it developing into a fabric sample 

New block 

 F10a

F10b 

F10c

F10d Using one triangle only cut using Fibonnacci sequence using a unit based on the perpendicular lengths

 F10e

F10f 

F10g 

F10h 

F10i 

These pieces are kept in a pack for further experimenting

F11a,b and c are designs made up of a larger block where the Fibonnacci sequence was applied but varying the sequence in an ad hoc manner
1,1,2,2,1,5,1,3,8

The pieces have been kept loose for further experimenting 
Golden Section

Here are two designs made using the principles of the Golden section

The first (GS1) is based on 1cm unit side measures increasing the squares in the proportions of 1,2,3,5,8,13,21- each square with tonal change from lighter to darker as go outwards, in an ante-clockwise direction

(The original piece contains a 21cm square folded over on the right to fit the A4 scan)

The second (GS2) a smaller design based on 1/2 cm unit alternating pattern and plain papers  

GS1

GS2

Of the two the first is more effective.
The second may have worked better using different patterned papers as the first or perhaps the effect would be better on a larger scale continuing the sequence, or putting in the diagonal line across each square to develop a spiral.

I can see there on many possibilities of using both the Fibonnacci sequences and Golden Section in developing pattern and design to translate into fabric.