#Tag · bonfire.cafe

[3/n] More artwork related to these substitution tilings, here with squares and rectangles of side ratios ρ and ρ² (titles in the ALT text). In the first one, all rectangles are in horizontal position.
#MathArt #algorithmicArt #AbstractArt #radiantnumber

Artwork "Arrival", rectangles and squares of shades of purple, pink and white, smaller in one blob and at the right part, with distinct colours.

Artwork "Encounter", rectangles and squares of shades of orange, green, blue, purple and white, smaller in two separate blobs, with distinct colours.

Artwork "Portal", rectangles and squares in shades of orange and grey, smaller at a centered circumference.

Artwork "Traffic", rectangles and squares in shades of red and blueish grey, smaller at the horizontal center line.

Dani Laura (they/she/he)

@DaniLaura@mathstodon.xyz · 3 weeks ago

Dani Laura (they/she/he)

@DaniLaura@mathstodon.xyz · 3 weeks ago

[2/n] Some artwork related to these substitution tilings, here with rectangles of side ratios ρ, ρ² and ρ³ (titles in the ALT text). All size ratios are integer powers of the radiant number.
#MathArt #algorithmicArt #AbstractArt #radiantnumber

Artwork "Warming light", rectangles of shades of yellow, red and grey, smaller at the center.

Artwork "Explosive Knowledge", rectangles of shades of yellow, magenta and purple, smaller at the center.

Artwork "Orange energy", orange and purplish grey rectangles, smaller at the center.

Dani Laura (they/she/he)

@DaniLaura@mathstodon.xyz · 3 weeks ago

[1/n] Continuing my work (see previous posts) about the geometric possibilities of the radiant number ρ (aka plastic ratio). Because it can serve as the base of a numeral system (just it and the golden ratio have this property among non-integers), every rectangle whose side ratio is a power of ρ can be decomposed into rectangles whose side ratio is a power of ρ. Particularly, if we take three consecutive powers of ρ we can make substitution tilings involving its corresponding rectangles. These properties are depicted in the first image. In the next images we see two possibilities regarding rectangles of ratios 1, ρ and ρ² (one just uses horizontal rectangles), and one for rectangles of ratios ρ, ρ² and ρ³. Of course any of these partitions, by rearranging/rotating/mirroring tiles, give many possible different tilings.
#Mathematics #geometry #tiling #mathart #radiantnumber

Substitutions for rectangles of side ratios ρ (purple colour), ρ² (green colour), and ρ³ (orange colour), .

Substitutions for rectangles of side ratios ρ⁰ = 1 (square, orange colour), ρ (purple colour) and ρ² (green colour), where rectangles are always put in horizontal position.

Substitutions for rectangles of side ratios ρ⁰ = 1 (square, orange colour), ρ (purple colour) and ρ² (green colour).

Seven colourful columns depict how each rectangle of ratio a power of the radiant number can be decomposed into rectangles of ratios in three consecutive powers of ρ.