Fibonacci

I’ve always been interested in symbols and patterns and particularly the patterns found in nature.

The work we are about to draw is one of those natural patterns that pops up all over the place.

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21… and continues.

The numeric pattern is created when the previous two numbers are added together to make the third number.

So, 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5 and so on.

The Fibonacci sequence continues indefinitely.

 

 

The Plant Kingdom

This pattern of numbers can be seen in nature.

Sunflower Heads

You will notice it in the placement of the seeds on the head of a sunflower.

The whorls spiral out in the Fibonacci sequence.

Pineapple

Another example of the Fibonacci sequence in plants is found on a pineapple where knobby things cycle up one way with eight spirals and the other way with thirteen spirals called interlocking helices.

These are just examples of how the Fibonacci numbers come through in the plant world.

 

The Animal Kingdom

One of the most obvious examples of the Fibonacci sequence in the animal kingdom is in the Nautilus shell.

The Nautilus is a seafaring animal that grows with chambers and measures out exactly the Fibonacci pattern.

I have a very small shell collection at home and within it I do have a Nautilus shell which I bought when I was in Mozambique.

There’s a photograph of it here.

This is the inspiration for this sketchbook piece that we are going to do together today.

Nautilus Shell

Supplies

I’m listing the art supplies I used to create this drawing, but I always urge you to use anything that you have at hand.

You do not have to go out and get these supplies.

You will probably have plenty of pens and papers in your home with which you can draw this sketch.

You Have What You Need

Don’t feel that you have to have all of this equipment and if you don’t you can’t do it.

Use the supplies that you have to hand.

You are an artist that’s why you are here.

Get your stuff out and let’s get started.

 

Drawing the Grid

We are taking the two numbers five and eight from the Fibonacci sequence.

We are going to draw a rectangle with that is eight blocks wide by five blocks deep.

It will depend on the size of your paper, but in my sketchbook, I drew a rectangle that was actually 2 x 8 which is 16 centimeters wide and 2 x 5 which is 10 centimeters deep.

If you are using inches, it might be easier to draw your box 8 inches by 5 inches or any combination of those numbers.

When you have your rectangle centred on your page it’s time to draw the grid.

Divide your rectangle into eight columns wide and five rows deep.

Drawing the Blocks

Look at my diagram to see how to further divide up your blocks.

On the left-hand side draw a thicker line after five columns.

Now looking on the right-hand part, which is now 3 columns wide, draw a thicker line 3 rows down.

From the bottom right corner draw a thicker line two rows over and two rows up.

Finally divide the last two into one cube each.

Keep looking at the block diagram to make sure that you are dividing your rectangle into the squares correctly.

Drawing the Curves

When drawing the lines with your compass make sure to press lightly.

You just want the line to be a guide we are not engraving on the page.

The pencil I have in my compass is a 2H pencil.

Make sure the tip of the compass point and the tip of the pencil are at the same place (when the compass is closed) before you start.

 

Steps

  • With your pencil compass place the point at the origin position shown by the red dot and draw two quarter circles over the one cube blocks.
  • Move your compass point to the origin position marked with the dot and draw a curve two blocks wide as shown.
  • Move your compass point to the third origin position shown and draw a curved line over three blocks.
  • Move your compass point into the final five block origin position and draw an arc five blocks wide as shown.

Dividing the Segments

Now we are going to divide each of the number blocks one, two, three and five into segments (like an orange) to indicate the growth of the shell.

Number One Blocks.

The number one blocks do not get divided as they are just one.

Number Two Blocks

The number two block division is from the origin point (where we put the compass in) draw a line at 45 degrees dividing the number two block into two segments.

Number Three Blocks

Considering the three blocks, place your protractor crosshairs at the origin point (where you put your compass point in) for the number three blocks, remember to reference the drawing.

We’re going to divide the number three block into three, so that will be 90-degrees divided by three will result in 30-degrees per segment.

Make a light mark at 30-degrees from the horizontal and 60-degrees from the horizontal on your page.

With a ruler, join the origin point for the number three blocks with the 30-degree and 60-degree mark lightly in pencil.

Do not extend the line past the curve.

Number 5 Blocks

We are going to divide the number five blocks into five segments.

Place your protractor cross hairs at the origin point for the number five block.

To divide 90-degrees by five each segment will be 18-degrees wide.

Counting up from the horizontal, make a light mark at 18-degrees and then one at 36-degrees (2 x 18 = 36).

Next, counting left from the vertical, make a light mark at 18-degrees and one at 36-degrees.

Take your ruler and lightly draw a line from the origin point to the marks you have just made.

You will draw four lines here thus dividing the five block into five segments.

Do not draw these lines past the curve of the shell.

Erase Marks

Lightly erase any pencil marks that are now unneeded and unnecessary before you start to color.

I also used a kneadable eraser and lifted quite a bit of the graphite from the page just leaving faint lines there as a guide.

Coloring the Shell

I chose to colour my Fibonacci shell in tones of yellow and the background in tones of blue.

Yellow and blue is always a great color combination to use in artwork and you can see this to great effect in Van Gogh’s “Starry, Starry Night” painting.

Take your time as this is the fun part.

Color in the background with different colors of blue.

Relax and color in each little segment withing each block carefully.

There will be many triangles and slivers of block now.

Finally, I went over with a heavy black pen and redrew the curve of the Fibonacci shell and the artwork outline.

Completed

Voila, and there is your completed sketch.

It is a fascinating shape as the Fibonacci shell continues to spiral outwards from the centre point.

This shape resonates with us as it is part of the natural world.

What Not to Do

When I first started drawing the Fibonacci shell, I couldn’t get it quite right because it’s quite a tricky pattern.

I tried several times, over a few days, to divide the shell because I wanted to you to see the striations and stripes on the shell which is how the actual Nautilus shell looks.

Now I’m going to show you my first few original efforts, so if for some reason you do make a botch, you will be happy knowing that it happens to everyone.

These first two drawings are examples of what not to do when trying to draw the Fibonacci shell.

The third one is correct.

Aspiring Artist Activity

In your sketchbook, please draw the Fibonacci shell by doing the following:

 

  • Measure the blocks carefully
  • Draw the curves carefully
  • Divide the segments carefully
  • Colour in and embellish your artwork as you see fit.

 

Share

Share your artworks on social with the hashtag #AHAFibonacci.

 

Alison Hazel

Author Bio

Alison Hazel is a mature woman who shares her ongoing journey about becoming an artist later in life. She creates simple art that anyone can make. She hopes to inspire you to reach your creative potential in the area that suits you.

Go here to read more about Alison's story.

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