Heptagon based patterns

SF5-04-col

 

Hi there,
today it’s all about heptagon stuff.And a bit of personal history in regard to that.As mentioned before on this blog I’m definitely no math-head,so,please bear with me and excuse the lack of correct terms and my rather simplistic approach.
Well then,let’s jump right into it.

7er-84

This is the first serious 7-fold pattern I came up with and was done in august 1984.At that time I had seen only very few examples of 7-fold patterns and one example of a crystallographic grid built from 6 heptagons (see below).The latter and the apparent lack of 7-fold patterns got me started to try to develop something of my own.And so I was pretty happy when I “found” this.

7er-VIII 84-orig

The original sketch/drawing.

7er84

The underlying grid that was used and can still be seen on the original sheet of paper.
Called it 7er/14er Kreissystem (circular system).Used the corners of one of the rhombuses you can split heptagonal things up to as centerpoints for the heptagonal elements of the pattern.

Please allow some remarks as to how I learned constructing patterns.
In the early eighties drawing knotwork/strapwork patterns became my main interest and I asked myself:”How could the ancient guys have done it?”
Since drawing circles is known for ages I decided to use a pair of compasses and a Geo-triangle as a straight edge.So far so good,but how are these patterns constructed?
In our local library I couldn’t find any books on constructing patterns.So I began to try to analyse patterns from photos and illustrations and gathered hints and stuff from every source available.
Meanwhile I know that there were books on patterns,but I just couldn’t find them back then.Maybe it was better anyway.That way I could develop my own approach(es).
Via the internet I got aware of the compasses and straight edge fraction and wondered that I never stumbled upon that earlier.Same goes for Hankin and his polygons in contact.

Over the years geometric attacks made me do 7-fold things from time to time.Not exclusively of course,but this is all about heptastuff,isn’t it?
Here are a few more examples in different styles.

7-7-b-1

Sort of  celtic knotwork.Drew just a seventh,photocopied it 7x and assembled it.

And a derivation of the above.Based on a way to connect 14 heptagons.

7-7-b-2A

 

And two of a different kind.Frac04

Frac05

Called those Fractals,because I was experimenting with some rules following Koch’s snowflake when I started this series.The second one has been used as a base for what comes later.

continued on page 2

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2 thoughts on “Heptagon based patterns

  1. I have to say, I am really impressed with your art! I do not traditionally have strong math skills, and to hear you describe yourself as not particularly mathematically gifted is inspiring to me. Thanks for making such beautiful geometric constructions!Keep up the great work.

    Like

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