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Branching Fractal 1


160 x 176 pixels, produced on a Vic-20 computer.
Typical graphics screen output from my Vic-20 computer
(includes a small cluster of 'pixel + no pixel + pixel', to show the size and aspect ratio of single pixels).

Generating such figures on my Vic-20 computer back in about 1989 gave me a genuine sense of excitement. The geometry in the basic idea was fascinating - drawing squares and triangles at various angles and sizes. I remember I needed to come up with a strategy for drawing the square with triangle on top of it from any 2 stored bottom corner points, and a way of storing all the resulting triangle points as bottom corner points for drawing the next generation of squares and triangles. And of course, computer programs rarely operate completely correctly the first time. To see the strategy and geometry realised felt exhilarating.

I was quite new to computer programming, and I largely taught myself through library books, computer manuals, and actually trying things. The Vic-20 turned out to be a pretty good computer for trying things.

The pixels that made up the graphics screen were not square, so I had to draw the figures using an aspect ratio for all vertical measurements to compensate for this.

 

 

 

Branching Fractal 2


320 x 352 pixels, produced on a Vic-20 computer.

This image used the full 320 x 352 pixel screen of my "BigArt" set of machine code routines, rather than just the small 160 x 176 pixel graphics screen for the first example above. The aspect ratio was set for 1:1 pixels.

 

 

Double-sized Version:


 

 

 

 

High Resolution Print 1


320 x 352 pixels, produced on a Vic-20 computer.

The high resolution prints shown here were produced by my Vic-20 computer (with some expansion memory added), and my own Epson dot-matrix printer. They use my own higher resolution graphics machine code routines (to plot pixels and draw lines, etc.), allowing me to produce line-based images to a maximum resolution of 1440 pixels by 2016 pixels on an A4 piece of paper from the dot-matrix printer.

I did this by firstly checking the figure on the 176 x 184 pixel screen of the Vic-20, then drawing an enlarged image on a ‘virtual’ horizontal graphics strip that was 1440 wide x 48 pixels high in size (requiring only about 8 KBytes of RAM), printing that virtual horizontal strip (exactly 2 high resolution graphics lines on the printer), ‘moving’ the position of the virtual graphics strip down in relation to the overall graphics page, redrawing the enlarged figure, printing the resulting lines to the printer, etc. This high resolution graphics technique took some time and management, but I was able to produce some very satisfying results from a computer with quite modest graphics resources.

 

 

 

High Resolution Print 2


The squares were stretched to become rectangles of similar proportions. This seemed to open up the space between the branches, but didn't change the angles of the branches.

 

 

 

High Resolution Print 3



A broccoli type form created by the specific proportions used for constructing the triangles. After doing several different images, I realised that the proportions used for generating the triangles on top of the rectangles determined the way that the branching would occur. One could think of the construction of the square and triangle as being set by the object’s ‘DNA’. The triangles’ proportions could be set with 2 parameters. In this way, a complex structure was determined by a small number of parameters.

 

 

 

High Resolution Print 4



I experimented with switching the orientation of subsequent triangles, and found this produced constructions with quite different characteristics.

 

 

 

Perspective Drawing of a Simple House Form


320 x 352 pixels, produced on a Vic-20 computer.

I came up with a strategy for producing drawings of models defined in 3-dimensions. This model only required 10 points and 15 lines between those points.

 

 

 

Double-sized Version:


 

 

 

 

Perspective Drawing of a Crystal Form 1


320 x 352 pixels, produced on a Vic-20 computer.

This was a much more complex form to enter, with 26 points and 56 lines. The 3D program makes use of an angle of rotation (view), an angle of altitude, and an image rotation angle.

 

 

Double-sized Version:


 

 


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