Publications by Patrick Ford
Dichotomy Sequence
Dichotomy Sequence plot and csv file generator dichotomy_sequence <- function(n_terms) { # Ensure the number of terms is positive if (n_terms <= 0) { return(NULL) } # Generate the sequence sequence <- 1 / (2^(1:n_terms)) return(sequence) } write_to_csv <- function(sequence, filename) { data <- data.frame(Term = 1:length(sequenc...
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Mandelbrot set
Plotting the Mandelbrot set # Load packages pacman::p_load(pacman,tidyverse,GGally,ggthemes,ggplot2,ggvis,httr,plotly,rio,rmarkdown,shiny,rgl) # Parameters x_range <- seq(-2, 0.7, length.out = 2000) # adjust the resolution by changing length.out y_range <- seq(-1.2, 1.2, length.out = 2000) max_iter <- 100 # Create a blank matrix to hold escape ti...
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The Logistic Map
Provides an R csv file generator of the Logistic Map, a mathematical model that can exhibit chaotic behaviour under certain conditions. Change the value of r (a positive number representing the growth rate) in the value section to create a different behavioural system. # Load packages pacman::p_load(pacman,tidyverse,GGally,ggthemes,ggplot2,ggvis,h...
278 sym
Benoît B. Mandelbrot - Bio
Benoît Mandelbrot Born on November 20, 1924, in Warsaw, Poland, Benoît B. Mandelbrot was a Polish-born, French and American mathematician known for his groundbreaking work in fractal geometry. Mandelbrot’s discoveries were revolutionary in showcasing that irregular, non-smooth objects, often found in nature, could be described mathematically. H...
1079 sym
The Mandelbrot set.
Plotting the Mandelbrot set # Load packages pacman::p_load(pacman,tidyverse,GGally,ggthemes,ggplot2,ggvis,httr,plotly,rio,rmarkdown,shiny,rgl) # Parameters x_range <- seq(-2, 0.7, length.out = 2000) # adjust the resolution by changing length.out y_range <- seq(-1.2, 1.2, length.out = 2000) max_iter <- 100 # Create a blank matrix to hold escape ti...
35 sym 1 img
DNA
The relationship between DNA, the Golden Ratio, and the Fibonacci Sequence The relationship between DNA, the Golden Ratio, and the Fibonacci Sequence is a fascinating topic that has attracted the attention of many researchers. DNA Structure and the Golden Ratio: The Double Helix: The structure of DNA is that of a double helix, a twisted ladder sh...
2288 sym
Scottish Deaths from Heart Disease
# Load packages pacman::p_load(pacman, tidyverse, GGally, ggthemes, ggplot2, ggvis, httr, plotly, rio, rmarkdown, shiny, rgl) # Import data X1 <- read.csv("dc0512a8-eb49-43b9-84f1-17ef95365d57.csv") ggplot(data=X1) + geom_col(mapping = aes(x = Year, y = NumberOfDeaths, color = Sex)) + facet_wrap(~Sex) ## Warning: Removed 761 rows containing mi...
18 sym Python (1075 sym/10 pcs) 5 img
Basic double helix
# Load packages pacman::p_load(pacman,tidyverse,GGally,ggthemes,ggplot2,ggvis,httr,plotly,rio,rmarkdown,shiny,rgl) # Golden ratio phi <- (1 + sqrt(5)) / 2 # Define the helix equations t <- seq(0, 10 * pi, length.out = 1000) r <- 1 c <- 0.1 * phi # Incorporating golden ratio into the z-increment x1 <- r * cos(t) y1 <- r * sin(t) z1 <- c * t x2 ...
9 sym
Basic double helix
# Load packages pacman::p_load(pacman,tidyverse,GGally,ggthemes,ggplot2,ggvis,httr,plotly,rio,rmarkdown,shiny,rgl) # Golden ratio phi <- (1 + sqrt(5)) / 2 # Define the helix equations t <- seq(0, 10 * pi, length.out = 1000) r <- 1 c <- 0.1 * phi # Incorporating golden ratio into the z-increment x1 <- r * cos(t) y1 <- r * sin(t) z1 <- c * t x2 ...
9 sym
Leonardo Fibonacci-bio.
Leonardo Fibonacci Overview Leonardo of Pisa, commonly known as Leonardo Fibonacci, was a medieval Italian mathematician who is best known for introducing the Fibonacci sequence to Western mathematics. Born in around 1175 in Pisa, Italy, and died circa 1240–50, Fibonacci played a crucial role in introducing the Western world to the decimal numbe...
2207 sym