PRINT.Rmd

```{r setup,include=FALSE}
# set the knitr options ... for everyone!
# if you unset this, then vignette build bonks. oh, joy.
#opts_knit$set(progress=TRUE)
opts_knit$set(eval.after='fig.cap')
# for a package vignette, you do want to echo.
# opts_chunk$set(echo=FALSE,warning=FALSE,message=FALSE)
opts_chunk$set(warning=FALSE,message=FALSE)
#opts_chunk$set(results="asis")
opts_chunk$set(cache=TRUE,cache.path="nodist/ignore/cache_")

#opts_chunk$set(fig.path="figure/",dev=c("pdf","cairo_ps"))
opts_chunk$set(fig.path="nodist/ignore/figures_",dev=c("png"))
#opts_chunk$set(fig.width=7,fig.height=7,dpi=300,out.width='700px',out.height='700px')
# try to make the files smaller ... 
opts_chunk$set(fig.width=7,fig.height=7,dpi=125,out.width='700px',out.height='700px')

# doing this means that png files are made of figures;
# the savings is small, and it looks like shit:
#opts_chunk$set(fig.path="figure/",dev=c("png","pdf","cairo_ps"))
#opts_chunk$set(fig.width=4,fig.height=4)
# for figures? this is sweave-specific?
#opts_knit$set(eps=TRUE)

# this would be for figures:
#opts_chunk$set(out.width='.8\\textwidth')
# for text wrapping:
options(width=124,digits=2)
opts_chunk$set(size="small")
opts_chunk$set(tidy=TRUE,tidy.opts=list(width.cutoff=50,keep.blank.line=TRUE))
library(ggplot2)
library(mazealls)
library(dplyr)
library(moments)
library(microbenchmark)
# chicken and egg dept:
# [![CRAN](http://www.r-pkg.org/badges/version/mazealls)](http://cran.rstudio.com/package=mazealls) 
# [![Downloads](http://cranlogs.r-pkg.org/badges/mazealls?color=brightgreen)](http://www.r-pkg.org/pkg/mazealls)
# [![Total](http://cranlogs.r-pkg.org/badges/grand-total/mazealls?color=brightgreen)](http://www.r-pkg.org/pkg/mazealls)
#[![Downloads](http://cranlogs.r-pkg.org/badges/mazealls?color=green)](http://www.r-pkg.org/pkg/mazealls)
#[![Total](http://cranlogs.r-pkg.org/badges/grand-total/mazealls?color=green)](http://www.r-pkg.org/pkg/mazealls)
# think lifecycle badges: https://github.com/r-lib/usethis/issues/48
```


# dodecagon maze

```{r simple-dodecagon,cache=TRUE,eval=TRUE,echo=FALSE,fig.keep='last'}
library(TurtleGraphics)
library(mazealls)
# dodecagon
set.seed(1234)
turtle_init(2200,2200,mode='clip')
turtle_hide()
turtle_up()
turtle_do({
  turtle_setpos(80,1100)
  turtle_setangle(0)
	 dodecagon_maze(depth=log2(27),unit_len=20,draw_boundary=TRUE,boundary_holes=c(1,7))
})
```
```{r simple-dodecagon-new,cache=TRUE,eval=TRUE,echo=FALSE,fig.keep='last'}
library(TurtleGraphics)
library(mazealls)
# dodecagon
set.seed(2301)
turtle_init(2200,2200,mode='clip')
turtle_hide()
turtle_up()
turtle_do({
  turtle_setpos(80,1100)
  turtle_setangle(0)
	 dodecagon_maze(depth=log2(27),unit_len=20,draw_boundary=TRUE,boundary_holes=c(1,7))
})
```

# Rhombic Dissections


```{r simple-octagon,cache=TRUE,eval=TRUE,echo=FALSE,fig.keep='last'}
library(TurtleGraphics)
library(mazealls)
# octagon
set.seed(4819)
turtle_init(2000,2000,mode='clip')
turtle_hide()
turtle_up()
turtle_do({
  turtle_setpos(75,1000)
  turtle_setangle(0)
	octagon_maze(log2(44),16,draw_boundary=TRUE,boundary_holes=c(1,5))
})
```

```{r simple-decagon,cache=TRUE,eval=TRUE,echo=FALSE,fig.keep='last'}
library(TurtleGraphics)
library(mazealls)
# decagon
set.seed(9019)
turtle_init(2200,2200,mode='clip')
turtle_hide()
turtle_up()
turtle_do({
  turtle_setpos(60,1100)
  turtle_setangle(0)
	decagon_maze(5,21,draw_boundary=TRUE,boundary_holes=c(1,6))
})

```

## Koch snowflake maze


```{r koch-flake,cache=TRUE,eval=TRUE,echo=FALSE,fig.keep='last'}
library(TurtleGraphics)
library(mazealls)
# koch flake
set.seed(1211)
turtle_init(1000,1000)
turtle_up()
turtle_hide()
turtle_do({
	turtle_left(90)
	turtle_forward(distance=200)
	turtle_right(90)
	turtle_backward(distance=300)
 	koch_maze(depth=4,unit_len=9)
})
```

```{r koch-meta-flake,cache=TRUE,eval=TRUE,echo=FALSE,fig.keep='last'}
library(TurtleGraphics)
library(mazealls)
# koch flake
set.seed(84910)
turtle_init(2000,2000,mode='clip')
turtle_up()
turtle_hide()
turtle_do({
	turtle_setpos(450,1000)
	turtle_setangle(60)
	ul <- 12
	dep <- 4
 	koch_maze(depth=dep,unit_len=ul,clockwise=TRUE,draw_boundary=FALSE)
	turtle_left(30)
	turtle_col('gray40')
	dropdown <- 1
	for (iii in c(1:6)) {
		if (iii==1) { bholes <- c(1,2) } 
		else if (iii==4) { bholes <- c(1,3) }
		else { bholes <- c(1) }
 		koch_maze(depth=dep - dropdown,unit_len=ul*(3^(dropdown - 0.5)),clockwise=FALSE,draw_boundary=TRUE,boundary_holes=bholes,
				boundary_hole_arrows=c(2,3))
		turtle_forward(3^(dep-1) * ul*sqrt(3))
		turtle_right(60)
	}
})
```

## Sierpinski Triangle

```{r sierpinski,cache=TRUE,eval=TRUE,echo=FALSE,fig.keep='last'}
library(TurtleGraphics)
library(mazealls)
set.seed(190)
turtle_init(2500,2500,mode='clip')
turtle_up()
turtle_hide()
turtle_do({
	turtle_setpos(50,1250)
	turtle_setangle(0)
	sierpinski_maze(unit_len=19,depth=7,draw_boundary=TRUE,boundary_lines=TRUE,boundary_holes=c(1,3),color1='black',color2='gray60')
})
```

### Sierpinski Carpet


```{r sierpinski-carpet,cache=TRUE,eval=TRUE,echo=FALSE,fig.keep='last'}
library(TurtleGraphics)
library(mazealls)
set.seed(12333)
turtle_init(800,1000)
turtle_up()
turtle_hide()
turtle_do({
	turtle_setpos(50,450)
	turtle_setangle(0)
	sierpinski_carpet_maze(angle=80,unit_len=8,width=90,height=90,
   draw_boundary=TRUE,boundary_holes=c(1,3),balance=1.5,color2='green')
})
```

```{r menger-sponge,cache=TRUE,eval=FALSE,echo=FALSE,fig.keep='last'}
library(TurtleGraphics)
library(mazealls)
set.seed(12333)
turtle_init(2000,2000,mode='clip')
turtle_hide()
turtle_up()
bholes <- list(c(1,2), c(1), c(2))
turtle_do({
 turtle_setpos(1000,1000)
 turtle_setangle(180)
 for (iii in c(1:3)) {
	 mybhol <- bholes[[iii]]
	 sierpinski_carpet_maze(angle=120,unit_len=11,width=81,height=81,
		 draw_boundary=TRUE,boundary_lines=c(1,2,3),num_boundary_holes=0,
		 boundary_holes=mybhol,balance=1.0,color2='green',
		 start_from='corner')
	 turtle_left(120)
 }
})
```

## Hexaflake 

```{r hexaflake,cache=TRUE,eval=TRUE,echo=FALSE,fig.keep='last'}
library(TurtleGraphics)
library(mazealls)
# hexaflake
set.seed(1144)
long_side <- 2400
inner_side <- long_side * sqrt(3)/2
sidelen <- long_side / 2
dep <- 3
ul <- floor(sidelen / (3^dep))
true_wid <- 2 * ul * 3^dep * sqrt(3)/2

turtle_init(ceiling(1.1 * inner_side),ceiling(1.1*long_side),mode='clip')
turtle_up()
turtle_hide()
turtle_do({
  turtle_setpos(0.5 * (ceiling(1.1 * inner_side) - true_wid),0.55*long_side)
  turtle_setangle(0)
	hexaflake_maze(depth=dep,unit_len=floor(sidelen / (3^dep)),draw_boundary=TRUE,color2='gray80')
})

```




## A rectangular spiral

```{r rect-spiral,cache=TRUE,eval=TRUE,echo=FALSE,fig.keep='last'}

rect_spiral <- function(unit_len,height,width,thickness=8L,angle=90,clockwise=TRUE,start_hole=FALSE) {
	if (start_hole) { 
		bholes <- 1
		fourl_dist <- height-thickness
	} else {
		bholes <- 4
		fourl_dist <- height
	}

	last_one <- (width < thickness)
	if (last_one) {
		blines <- 1:4
		bholes <- c(3,bholes)
	} else {
		blines <- c(1,2,4)
	}
	blocs <- - sample.int(n=thickness,size=4,replace=TRUE)

	parallelogram_maze(unit_len=unit_len,
										 height=thickness,width=fourl_dist,
										 angle=180-angle,
										 start_from='corner',clockwise=clockwise,
										 draw_boundary=TRUE,boundary_lines=blines,
										 boundary_holes=bholes,boundary_hole_locations=blocs,
										 end_side=3)
	if (clockwise) { turtle_left(angle) } else { turtle_right(angle) }

	if (!last_one) {
		rect_spiral(unit_len,height=width,width=height-thickness,
								thickness=thickness,angle=180-angle,clockwise=clockwise,start_hole=FALSE)
	}
}

set.seed(1111)
turtle_init(2500,2500,mode='clip')
turtle_up()
turtle_hide()
turtle_do({
	turtle_setpos(300,50)
	turtle_setangle(270)
	rect_spiral(unit_len=20,110,90,thickness=15,angle=80,start_hole=TRUE)
})
```


## A double rectangular spiral

```{r rect-double-spiral,cache=TRUE,eval=TRUE,echo=FALSE,fig.keep='last'}
double_spiral <- function(unit_len,height,width,thickness=8L,angle=90,clockwise=TRUE,start_hole=TRUE,color1='black',color2='black') {
	len1 <- height - thickness
	bline1 <- c(1,2,4)
	bline2 <- c(1,3,4)
	bhole1 <- c(2)
	if (start_hole) { 
		len2 <- len1
		bline2 <- c(bline2,2)
		bhole1 <- c(bhole1,4)
	} else {
		len2 <- len1 - 2 * thickness
	}
	blocs1 <- - sample.int(n=thickness,size=4,replace=TRUE)
	blocs2 <- - sample.int(n=thickness,size=4,replace=TRUE)
	last_one <- (min(len1,len2) <= 0) || (width <= 2*thickness)
	if (last_one) {
		bhole2 <- c(4)
	} else {
		bhole2 <- c(3)
	}
	if (start_hole) { 
		bhole2 <- c(bhole2,2)
	}
	second_stripe <- ((len2 > 0) && (width > thickness))

	if (len1 > 0) {
		turtle_col(color1)
		parallelogram_maze(unit_len=unit_len,
											 height=len1,width=thickness,
											 angle=angle,
											 start_from='corner',clockwise=clockwise,
											 draw_boundary=TRUE,boundary_lines=bline1,
											 boundary_holes=bhole1,boundary_hole_locations=blocs1,
											 end_side=ifelse(len2 > 0,3,2))
		if (second_stripe) {
			wid2 <- min(thickness,width-thickness)
			turtle_col(color2)
			parallelogram_maze(unit_len=unit_len,
												 height=len2,width=wid2,
												 angle=180-angle,
												 start_from='corner',clockwise=!clockwise,
												 draw_boundary=TRUE,boundary_lines=bline2,
												 boundary_holes=bhole2,boundary_hole_locations=blocs2,
												 end_side=4)
			turtle_col(color1)

			turtle_forward(unit_len*(thickness+wid2))
			if (clockwise) {
				turtle_right(180-angle)
			} else {
				turtle_left(180-angle)
			}
			turtle_forward(unit_len*thickness)
			if (clockwise) {
				turtle_right(angle)
			} else {
				turtle_left(angle)
			}
		}
	}
	next_height <- width
	next_width <- ifelse(start_hole,height,height-2*thickness)

	if (last_one) {
		if (second_stripe) {
			parallelogram_maze(unit_len=unit_len,height=next_height,width=thickness,
												 start_from='corner',
												 angle=180-angle,clockwise=clockwise)
		} else {
			parallelogram_maze(unit_len=unit_len,height=next_height,width=thickness,
												 start_from='corner',
												 angle=angle,clockwise=!clockwise)
		}
	} else {
		double_spiral(unit_len,height=next_height,width=next_width,thickness=thickness,
									angle=180-angle,clockwise=clockwise,start_hole=FALSE,
									color1=color1,color2=color2)
	}
}

set.seed(1111)
turtle_init(2500,2500,mode='clip')
turtle_up()
turtle_hide()
turtle_do({
	turtle_setpos(300,50)
	turtle_setangle(0)
	double_spiral(unit_len=20,height=100,width=100,thickness=10,angle=80,start_hole=TRUE,color2='gray40')
})
```


## A boustrophedon


```{r rect-boustrophedon,cache=TRUE,eval=TRUE,echo=FALSE,fig.keep='last'}

boustro <- function(unit_len,height,width,thickness=8L,angle=90,clockwise=TRUE,start_hole=TRUE,balance=0) {
	if (start_hole) { 
		bholes <- c(1,3)
		blines <- 1:4
	} else {
		bholes <- c(1,3)
		blines <- 2:4
	}

	last_one <- (width < thickness)
	blocs <- sample.int(n=thickness,size=4,replace=TRUE)

	parallelogram_maze(unit_len=unit_len,
										 height=height,width=thickness,
										 angle=angle,
										 balance=balance,
										 start_from='corner',clockwise=clockwise,
										 draw_boundary=TRUE,boundary_lines=blines,
										 boundary_holes=bholes,boundary_hole_locations=blocs,
										 end_side=3)
	if (!last_one) {
		boustro(unit_len,height=height,width=width-thickness,thickness=thickness,angle=180-angle,clockwise=!clockwise,start_hole=FALSE,balance=balance)
	}
}

turtle_init(2500,2500,mode='clip')
turtle_up()
turtle_hide()
turtle_do({
	turtle_setpos(100,50)
	turtle_setangle(0)
	boustro(unit_len=26,height=82,width=80,thickness=8,angle=85,balance=1.5)
})
```