Safe Haskell | None |
---|---|

Language | Haskell98 |

- sprott_tbl_2_1 :: [(Char, Int, Double)]
- sprott_coef :: Char -> Maybe Double
- sprott_coef_err :: Char -> Double
- with_delayed :: Int -> [t] -> [(t, t)]
- quadratic_1 :: Num a => a -> a -> a -> a -> a
- quadratic_1l :: Num a => [a] -> a -> a
- quintic_1 :: Num a => a -> a -> a -> a -> a -> a -> a -> a
- quintic_1l :: Num a => [a] -> a -> a
- general_1l :: Num a => [a] -> Maybe (a -> a)
- quadratic_2 :: Num t => t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> (t, t) -> (t, t)
- quadratic_2l :: Num t => [t] -> (t, t) -> (t, t)
- cubic_2 :: Num t => t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> (t, t) -> (t, t)
- cubic_2l :: Num t => [t] -> (t, t) -> (t, t)
- general_2l :: Num t => [t] -> Maybe ((t, t) -> (t, t))
- quadratic_3 :: Num t => t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> (t, t, t) -> (t, t, t)
- quadratic_3l :: Num t => [t] -> (t, t, t) -> (t, t, t)
- general_3l :: Num t => [t] -> Maybe ((t, t, t) -> (t, t, t))
- sphere_proj :: (Floating t, Ord t) => [(t, t)] -> [(t, t)]
- plot_code_1 :: Int -> Int -> Double -> (Code, Annotation) -> IO ()
- plot_code_2 :: Bool -> Int -> (Double, Double) -> (Code, Annotation) -> IO ()
- plot_code_3 :: Int -> (Double, Double, Double) -> (Code, Annotation) -> IO ()
- type Code = String
- type Annotation = String
- codes_1 :: [(Code, Annotation)]
- codes_2 :: [(Code, Annotation)]
- codes_3 :: [(Code, Annotation)]
- logistic :: Num a => a -> a -> a
- henon :: Num t => t -> t -> (t, t) -> (t, t)

# Coding Table

sprott_tbl_2_1 :: [(Char, Int, Double)] Source

Table 2-1. ASCII character set and associated coefficient values (p.28)

sprott_coef :: Char -> Maybe Double Source

Lookup coeffient at `sprott_tbl_2_1`

.

sprott_coef 'M' == Just 0

sprott_coef_err :: Char -> Double Source

`fromJust`

of `sprott_coef`

.

# General forms

with_delayed :: Int -> [t] -> [(t, t)] Source

Pair each elements with the element *n* places further along.

with_delayed 3 [1..9] == [(1,4),(2,5),(3,6),(4,7),(5,8),(6,9)]

quadratic_1 :: Num a => a -> a -> a -> a -> a Source

General one-dimensional quadratic iterated map (Equation 2A, p.25)

quadratic_1l :: Num a => [a] -> a -> a Source

List (*l*) variant of `quadratic_1`

.

quintic_1 :: Num a => a -> a -> a -> a -> a -> a -> a -> a Source

General one-dimensional quintic iterated map (Equation 2E, p.41)

quintic_1l :: Num a => [a] -> a -> a Source

List (*l*) variant of `quintic_1`

.

general_1l :: Num a => [a] -> Maybe (a -> a) Source

Generalised one-dimensional iterated map.

quadratic_2 :: Num t => t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> (t, t) -> (t, t) Source

General two-dimensional iterated quadratic map (Equation 3B, p.53)

quadratic_2l :: Num t => [t] -> (t, t) -> (t, t) Source

List (*l*) variant of `quadratic_2`

.

cubic_2 :: Num t => t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> (t, t) -> (t, t) Source

General two-dimensional iterated cubic map (Equation 3F, p.80)

general_2l :: Num t => [t] -> Maybe ((t, t) -> (t, t)) Source

Generalised two-dimensional iterated map.

quadratic_3 :: Num t => t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> t -> (t, t, t) -> (t, t, t) Source

General three-dimensional iterated quadratic map (Equation 4A, p.147)

quadratic_3l :: Num t => [t] -> (t, t, t) -> (t, t, t) Source

List (*l*) variant of `quadratic_3`

.

general_3l :: Num t => [t] -> Maybe ((t, t, t) -> (t, t, t)) Source

Generalised three-dimensional iterated map.

# Projections

sphere_proj :: (Floating t, Ord t) => [(t, t)] -> [(t, t)] Source

Projection onto sphere (Equation 3G, p.107)

# Code Plotting

plot_code_1 :: Int -> Int -> Double -> (Code, Annotation) -> IO () Source

Plot one-dimensional code, *m* is delay, *n* is iteration degree, *i* is initial value.

plot_code_2 :: Bool -> Int -> (Double, Double) -> (Code, Annotation) -> IO () Source

Plot two-dimensional code, *n* is iteration degree, *i* is initial value.

plot_code_3 :: Int -> (Double, Double, Double) -> (Code, Annotation) -> IO () Source

Plot three-dimensional code, *n* is iteration degree, *i* is initial value.

# Co-efficient codes.

A code is a string. The set of book codes are at: http://sprott.physics.wisc.edu/fractals/bookdisk/BOOKFIGS.DIC and there is a further set of codes at: http://sprott.physics.wisc.edu/fractals/bookdisk/SELECTED.DIC

type Annotation = String Source

codes_1 :: [(Code, Annotation)] Source

One-dimensional codes.

plot_code_1 5 12500 0.1 (codes_1 !! 7)

codes_2 :: [(Code, Annotation)] Source

Two-dimensional codes.

plot_code_2 False 25000 (0.1,0) (codes_2 !! 25)

codes_3 :: [(Code, Annotation)] Source

Three-dimensional codes.

plot_code_3 15000 (0.1,0,0) (codes_3 !! 1)