Hans Dehlinger

University of Kassel, Germany
Berlin / Kassel, Germany

The drawings are constructed with the numbers 1, 1, 2, 3, and 5 from the Fibonacci sequence. Hence they are mathematically simple, because this sequence is well known. All drawings make use of a seed-figure (F1) that is generated with this numbers. Different, premeditated generative rules and steps, using standard geometric transformations like rotate, scale, shift and reflect are then applied to the seed figure. The resulting images are submitted to a pen-plotter and are mechanically drawn with a pencil on paper.

The rationale behind these experiments is to use a mathematically based starting point, and continue with intuitively, but nevertheless rigorous formulated rules. As a result we expect a series of graphic figures that are related to each other but can stand in their own right. Although simple, they should display a distinctive constructive strength.

The pen-plotted lines differ significantly from printed lines, which is an important and a wanted side effect.

Imagesize 16 x 16 cm
Plotterdrawing, pencil on paper

All images are based on a seed figure (called F1), generated as follows:

1. Construct a grid with 12 x 12 units (12 = 1+1+2+3+5).

2. Starting from the bottom left corner, moving upwards in the grid, draw adjacent rectangles with 1, 1, 2, 3, 5 units in height.

3. Divide each rectangle by a tilted line: Start on the bottom horizontal and end on the top horizontal of each rectangle. Move each starting point from the left border by 1, 1, 2, 3, 5 grid-units to the right, and move each respective end point by 1, 1, 2, 3, 5 grid-units from the right border to the left.

F1 is transformed into F2 by repeating the tilted lines in the rectangles of F1 with 2, 3, and 5 units in height, resulting in 2, 3, and 5 tilted lines respectively while moving to the right one unit for each repeated line.

Generation of image Fibo_3B:

From F1 get F2; place a copy of F2 on top of F2 and shift it one grid-unit down and to the right.

Imagesize 16 x 16 cm
Plotterdrawing, pencil on paper

Generation of image Fibo_rot+rflt:

Input seed figure F1 and rotate it by 90°; reflect along the vertical axis.

Assign appropriate line-weights.

Imagesize 16 x 16 cm
Plotterdrawing, pencil on paper

Generation of image Fibo-a1.2:

From F1 get F2; place a copy of F2 onto F2 and shift it 6 grid-units to the left to get F2´.

Move a copy of F2´ five units down and place it onto F2´ to get F2´´.

Rotate F2´´ by –90° and reflect horizontally.

Set appropriate line-weights.