Posts

Using cellular automata for retro maps

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There are several cellular automata map examples online but very few resemble mine.  I use fewer generations,  initial seeds commonly of between  1 - 5% and   a variety of alternative life rules that I have experimented with over the years. Programs used: MCell http://www.mirekw.com/ca/ Mirek Wojtowicz (Mirosław Wójtowicz) Irfanview (for batch conversion of files) https://www.irfanview.com/ Irfan Skiljan Jasc Paintshop Pro 7 (for flood fill and borders) Image to Ascii Converter https://www.softpedia.com/get/Multimedia/Graphic/Image-Convertors/Bitmap-to-Ascii-converter.shtml Peter Bone The larger images of 1280x960 pixels (each pixel representing a 5x5 or 8x8 user defined graphic block) are scaled down versions of entire maps.  Those below them are a 3x zoom section to show the scale.  I purposely chose a grid size of 160x96 pixels as games (known as homebrews) are still being produced for the Mattel Intellivision games console (now owned by Atari). Leg...
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Sheep's head and anchor

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The last of four short articles on mirror symmetric tiles. This is another of Ortwin Schenker's ideas.  The sheep's head and anchor are from Bob Nungester's treasure trove of computational shapes.   The anchor is composed of a stopcock and two bowties (below, far right): Arnaud  Chéritat  was the first to find a periodic tiling (below left).  I noticed it could be broken down into a smaller component  comprised of two sheep's heads and one anchor : The example below shows all possible legitimate configurations when combining two of these motifs.  It can be thought of as a single polygon, as it does not use reflections: Many periodic tilings are possible; two examples below: And another with a tree motif: Here are two attempts of a hexagon without any gaps.  The motifs are still intact although less obvious: Some familiar shapes disguised as voids (highlighted in white): These drawings were created using the latest stable version of Arnaud Ché...
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Mystic and rotor

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Continuing on the theme of symmetric figures, Ortwin Schenker suggested combining a Mystic (two Spectres) with a rotor: both are non-tilers.  Arnaud Chéritat was the first to respond with a periodic tiling.  He used a motif of three Mystics and one rotor.  Gaps are filled with single rotors: A cut-down version of Arnaud's motif can be used to create more complex periodic tilings.  The square unit can be of any size and with different arrangements: There are eight different combinations of the 'chair' tromino: Any one of these can be assembled to produce a nonperiodic tiling using a substitution rule: A beautiful flower motif: This simple motif produces an attractive spiral: These drawings were created using the latest stable version of Arnaud Chéritat's applet: https://www.math.univ-toulouse.fr/~cheritat/AppletsDivers/Monotile/generic/v4.3/
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Seesaw and hexagon

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The second of four short write-ups on curious pairings of symmetric tiles. We start with a regular hexagon and a non-tiler borrowed from Bob Nungester's computational heap  which I named the seesaw. In combination they can produce an attractive periodic tiling: Hexagons will never touch one another but their orientations may differ (e.g., those highlighted in green).  I have also coloured in a few randomly selected groups of 4, 5 and 6 seesaws  surrounding hexagons (in red)  to give some idea of complexity: Below is (I believe) a picture listing of all unique coronas surrounding a hexagon that may appear in a tiling. A couple of six-fold symmetry examples: Two and three-fold symmetry.  All these tiling examples can easily continue: These drawings were created using the latest stable version of Arnaud Chéritat's applet: https://www.math.univ-toulouse.fr/~cheritat/AppletsDivers/Monotile/generic/v4.2/
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Squid and glider

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The first of four short articles where I combine two shapes with mirror symmetry to form tilings. In the first example, I chose one of Bram Cohen's polygons which I have named the squid.  This shape  can tile easily (and rather boringly) on its own unless you include hexagonal formations of six squids (in grey) as shown below:  With this in mind, the squid now behaves differently and relies on  another shape which I have named the glider (in white), in order to tile the plane.  The two tiles in combination can produce an attractive periodic pattern  which can continue without limits and exhibits a structure that is possibly unique. The six squids that make up the smaller hexagons can be positioned in a clockwise or anticlockwise direction but everything else remains static: These drawings were created using the latest stable version of Arnaud Chéritat's applet: https://www.math.univ-toulouse.fr/~cheritat/AppletsDivers/Monotile/generic/v4.1/
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