SELF-SIMILARITY, FRACTALS, APPLICATION OF INNOVATIVE GEOMETRY
This page will be a collection of fractal applications until it reaches the critical volume in order to become a dedicated web-page.
Fractal city:
The competition for an innovative design of Black Rock city, the playground of the famous Burning Man festival, made me keen of drawing the plan below. It uses the 99's Black Rock city design as a city-model and then "pentagonism" is applied.
The pentagon is the city boundary and this influenced the work. The spine of the city is made of 1st iteration {5/1}-star-polygonal fractal (red pentagons), then the 2nd iteration (blue pentagons) and finally the fifth iteration (black pentagons filled with yellow). The yellow pentagons are computed by computer, however everything else is fitted by hand and processed with Incscape.
Fractal coordinate system is applied and every pentagon has its unique number (except the Camp Center). The counting starts with 0 from the central pentagon, then rotates clockwise until it reaches its 6th element (non central fractal elements have 7 pentagons). For clarity, the Element 1 which is dummy is enumerated. It is divided by 7 pentagons, (1,0) (1,1) (1,2) (1,3) (1,4) (1,5) and (1,6) where (1,3) is also divided by (1,3,0) (1,3,1) (1,3,2) (1,3,3) (1,3,4) (1,3,5) and (1,3,6). The same logic could be applied for the enumeration of all the Pentagons at any scale.
The Burning Man is placed at (0,0) pentagon and is drawn as the Vitruvian Man of Da Vincy reminding us that the golden ratio is all over the city plan. Indeed, the scaling factor of the pentagons is 1/phi squared. This is the scaling rule of the self-similarity of the city plan that connects the pentagonal boundary of the site with each individual pentagonal element of Black Rock. The Vitruvian Man is also reminding us that the golden ratio self-similarity continues all the way to the human proportions of the Black Rock citizens. Hence, the city is designed as a natural extension of its inhabitants.
The competition for an innovative design of Black Rock city, the playground of the famous Burning Man festival, made me keen of drawing the plan below. It uses the 99's Black Rock city design as a city-model and then "pentagonism" is applied.
The pentagon is the city boundary and this influenced the work. The spine of the city is made of 1st iteration {5/1}-star-polygonal fractal (red pentagons), then the 2nd iteration (blue pentagons) and finally the fifth iteration (black pentagons filled with yellow). The yellow pentagons are computed by computer, however everything else is fitted by hand and processed with Incscape.
Fractal coordinate system is applied and every pentagon has its unique number (except the Camp Center). The counting starts with 0 from the central pentagon, then rotates clockwise until it reaches its 6th element (non central fractal elements have 7 pentagons). For clarity, the Element 1 which is dummy is enumerated. It is divided by 7 pentagons, (1,0) (1,1) (1,2) (1,3) (1,4) (1,5) and (1,6) where (1,3) is also divided by (1,3,0) (1,3,1) (1,3,2) (1,3,3) (1,3,4) (1,3,5) and (1,3,6). The same logic could be applied for the enumeration of all the Pentagons at any scale.
The Burning Man is placed at (0,0) pentagon and is drawn as the Vitruvian Man of Da Vincy reminding us that the golden ratio is all over the city plan. Indeed, the scaling factor of the pentagons is 1/phi squared. This is the scaling rule of the self-similarity of the city plan that connects the pentagonal boundary of the site with each individual pentagonal element of Black Rock. The Vitruvian Man is also reminding us that the golden ratio self-similarity continues all the way to the human proportions of the Black Rock citizens. Hence, the city is designed as a natural extension of its inhabitants.
Outcome:
This design seemed to be too technical and confusing! However, on October, 27, 2015 just a month before I put the Vitruvian Man in the middle, the theme of Burning Man 2016 had been announced (the date of the file I've used for the design is December, 20, 2015). And guess what, it had been Da Vinci's Workshop
https://journal.burningman.org/2015/10/burning-man-arts/brc-art/burning-man-2016-da-vincis-workshop/
Moreover, on September, 3, 2016 the Vitruvian Man was really burned in the middle of the Black Rock City http://www.rgj.com/story/life/arts/burning-man/2016/09/04/man-goes-up-flames-burning-man-nears-end/89859818/ This coincidence makes me happy because I was led only by the geometrical shape of the pentagram that really encloses the desert area of the event. Surprisingly, this resulted in the same decision as the organizers about who has to be at the balefire.
You can see all other designs here https://brcmup.org/