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Hat types from equilateral Cairo pentagons

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I created these shapes in the grid below, using the  Polyform Puzzle Solver by Jaap Scherphuis.  I then reconstructed them in VectorEngineer Pro-Tools using angles of 69.295, 90 and 114.295 that were suggested to me by Jaap. The DXF files were converted using Bob Nungester's small but effective DXF to TXT utility, for use in Arnaud Chéritat's dedicated tiling applet (links at the foot). The Som brero:   This tile  can simulate the chair tiling if reflections are allowed: Crumpled hat: A group of four tiles can produce an attractive periodic tiling: A six-tile motif combined with its reflection, which is also rotated, produces a striped pattern: Beret: This tile when used with its reflection, produces strips that can be glued together in different ways.  However, there's only one configuration that the beret can tile if reflections are not used. Novelty hat: This polygon can produce misshapen mesh-like structures, if allowing reflections. Links: Bob Nunges...
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Scottie dog, rabbit and donkey

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I made up these shapes by overlapping and creating voids from other Spectre related polygons.  From left to right, the Scottie dog,   rabbit   and donkey.  They either don't need or won't work with their reflection, so are essentially single tiles: Later research revealed that all of these polygons can be constructed with Bram Cohen's ducks and rotary blades. The Scottie dog is cute but the most versatile of the three is the  rabbit .  It can do everything and more!  Putting only two together back to back creates a small hexagon-like figure: Each ring can be constructed in three different configurations.  These motifs can be filled in a variety of ways and are periodic, even if one was the size of a planet: Other central cores include feet in, heads in and chaotic: It seems that spirals can have any number of arms.  Those shown are 2, 3, 5, 11 and 12: Anthills.  The surrounding area can be filled in all manner of ways: Start of...
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Fractal eXtreme

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I've been using Fractal eXtreme of late, creating many zoomed images of Mandelbrot variants.  These include Perpendicular Mandelbrot (top right),  Burning Ship, Perpendicular Burning Ship,  Buffalo and Perpendicular Buffalo (bottom right) . The program was last updated in January 2016  but is amazingly fast and has antialiasing options when generating/previewing fractal zooms.  More information here: https://www.cygnus-software.com/ The preset palettes in Fractal eXtreme are mainly made up of primary colours (garish) which I didn't particularly like so I opted for greyscale.  I later modified it to produce a dark sepia-like duotone. Mandelbrot  (we all know and love). Perpendicular Mandelbrot Burning Ship Perpendicular Burning ship Buffalo Perpendicular Buffalo More Perpendicular Mandelbrot and Perpendicular Burning Ship images (in slideshow format) on my website: https://the-orangery.weebly.com/perpendicular-mandelbrot.html https://the-orangery.weebly...
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