Thu, 01 Feb 2024 11:27:27 +0000 Thu, 01 Feb 2024 11:27:27 +0000 https://www.grasshopper3d.com/photo/phoenix-fractal?context=user by Matous Stieber Phoenix fractal was discovered by Shigehiro Ushiki; in 1998 in paper published in the 'IEEE Transactions on Circuits and Systems' journal. The Phoenix fractals are modifications of the Mandelbrot and Julia sets. The initial Phoenix fractal formula was z(n+1) = z(n)a + c*z(n) b + p*z(n-1) with the parameters of c=0.5667 and P=-0.5. Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/simurgh-fractal?context=user by Matous Stieber Simurgh fractal z(n+1) = z(n) a + c*z(n)b + p*z(n-1) + q*z(n-2); subset of the Simurgh fractals are the Phoenix fractals Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/nova-fractal?context=user by Matous Stieber The Nova fractal was created by Paul Derbyshire while estimating the Newton fractals. Paul Derbyshire modified the Newton's method in order to improve the the rate of convergence. The Nova fractal is derived from this equation zn+1 = zn - R * f(zn) / f '(zn) while the initial function was f(z) = zp-1, and therefore the equation that is iterated  zn+1 = zn - R (znp - 1) / (p znp-1) + c Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/mandelbrot-set-4?context=user by Matous Stieber The intention of the research was to create the Mandelbrot Set by using custom ghPython Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/burning-ship-1?context=user by Matous Stieber The intention of the research was to create the Burning ship fractal by using custom ghPython component in Grasshopper for Rhino. Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/burning-ship?context=user by Matous Stieber The intention of the research was to create the Burning ship fractal by using custom ghPython component in Grasshopper for Rhino. Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/julia-set-of-sin-z-for-c-1-0-2i?context=user by Matous Stieber The intention of the research was to create the Julia Set of sin(z) for c=1+0.2i by using custom ghPython component in Grasshopper. Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/julia-set-3?context=user by Matous Stieber The intention of the research was to create the Julia Set for c=-0.74543+0.11301i by using custom ghPython component in Grasshopper. Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/julia-set-1?context=user by Matous Stieber The intention of the research was to create the Julia Set for c=-0.512511498387847167+0.521295573094847167i by using custom ghPython component in Grasshopper. Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/mandelbrot-set-3?context=user by Matous Stieber The intention of the research was to create the Mandelbrot Set by using custom ghPython component in Grasshopper. Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/mandelbrot-set-2?context=user by Matous Stieber The intention of the research was to create the Mandelbrot Set by using custom ghPython component in Grasshopper. Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/mandelbrot-set-1?context=user by Matous Stieber The intention of the research was to create the Mandelbrot Set by using custom ghPython component in Grasshopper. Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/julia-set-2?context=user by Matous Stieber The intention of the research was to create the Julia Set for c=0.28+0.008i by using custom ghPython component in Grasshopper. Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/julia-set?context=user by Matous Stieber The intention of the research was to create the Julia Set for c=-0.8+0.156i by using custom ghPython component in Grasshopper. Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/the-barnsley-fern?context=user by Matous Stieber The intention of the research was to create the Barnsley Fern by using custom ghPython component in Grasshopper. The Barnsley Fern, described by the British mathematician Michael Barnsley, refers to an iterated function system (IFS). Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/mandelbrot-set?context=user by Matous Stieber The intention of the research was to create the Mandelbrot Set by using custom ghPython component in Grasshopper. Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/diffusion-limited-aggregation?context=user by Matous Stieber The intention of the research, inspired by Andy Lomas (SIGGRAPH 2006), was to create the Diffusion-Limited Aggregation with constraints (without additional processing of the geometry by marching cubes algorithm) by using custom ghPython component in Grasshopper. Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber https://www.grasshopper3d.com/photo/diffusion-limited-aggregation-2?context=user by Matous Stieber The intention of the research, inspired by Andy Lomas (SIGGRAPH 2006), was to create the Diffusion-Limited Aggregation with constraints (additional processing of the geometry by marching cubes algorithm) by using custom ghPython component in Grasshopper. Matous Stieber https://www.grasshopper3d.com/profile/MatousStieber