Plotter is oettinger-physics.de's empirical plotting utility, a tool to draw function graphs or calculate function values at certain points. Plotter can be used to produce images showing up to three curves of given functions and ten points of interest in a simple cartesian system.
Quick-n-dirty usage: enter one ore more functions (mathematical expressions) into the fields on the right and gently press the button labeled 'Draw' to see the corresponding curves in an image on the left side.
The functions f(x), g(x), h(x) to plot and some specials can be declared in text inputs on the right hand side, a color (in hex notation) and some options can be set: a function term can be printed out in the plot, points calculated to draw the curve can be shown as dots or interconnected and the inside or outside of each curve can be filled with the selected color.
The special options settable on the right are
hull | is the outer function in a function composition.
The results of the inner functions f(x), g(x) and h(x) will pointwise be used
as a variable Y for the outer (hull) function H(Y) or in math notation
(H ∘ f)(x), (H ∘ g)(x) and (H ∘ g)(x). This is similar to a substitution, e.g. sin(Y) defined as hull function will plot the sine of each defined function. Consider using 2*exp(-.5*Y) as hull, x as f(x) and x^2 as g(x) - you will get this plot of 2*exp(-.5*x) and 2*exp(-.5*x^2). |
Q | Substitution mechanism. An expression can be defined and used as a substitute for the special variable Q in function terms. A function value will be calculated after calculation of Q, so f(x) = 2 - Q with Q = 1+x really means f(x) = 2 - (1+x). |
df/dx (derivative) | shows the derivated graph. In the legend, this will be displayed as f'(x)=[...]'. |
∫f(x)dx (integral) | shows the cumulative function in the plotted interval (integrate over ...). Calculated function values are cumulated one after another and the constant value C is added (if set). The integrated term will be named F(x)=S[...]. |
For all functions and numbers, you can use mathematical expressions which may contain function names, constant names and combinations of the following symbols:
x | is treated as variable name in functions f(x) |
0-9 | Numbers like 123.45, input values
are hardly restricted (as long as you don't plan to use more than
some hundred digits). The output value (result) at a non-log scale
is restricted to +/-100000 which is also the maximum value for both
axes. Large or small numbers may be written in scientific Notation (the standard index form like 2.5E20 for 2.5·10^{20}), decimal digits are exact up to a number of 12. |
. , | point or comma as decimal separators: 1.5 is the same as 1,5 |
+-*/ | basic arithmetic operations (when multiplying numbers and variable names, the operator '*' can be omitted, i.e. 2x = 2*x) |
( ) [ ] { } < > | brackets, e.g. {[(1+x)/(2-x)+1]*3}/(2*x^2). As common in mathematics, the type of brackets used does not matter. |
# | is used as separator for functions accepting multiple input values, e.g. scir(x#2) |
asy | show a vertical asymptote at a fixed value x, e.g. asy(1) or asy(e) |
Plotter is aware of some common constants that can be used in formulas, expressions and all numerical input. So e^x is the same as exp(x) and a plot can easily be drawn from -π to π by setting the plotting range from -pi to pi.
e | Euler's number: 2.718281828459 |
pi | π, Pi: 3.1415926535898 |
pi2 | π/2, Pi/2: 1.5707963267949 |
sq2 | square root of 2: 1.4142135623731 |
go | relation of the golden ratio: 1.6180339887499 |
d | Feigenbaum constant delta: 4.6692016091030 |
Plotter knows many interesting functions, nested ones like sin(pow(x#2/3)) or polynomials like 2*x^3-4*x^2+x+1 should work without problems. The order of arguments in functions with multiple variables (e.g. norm) does not matter, the standard position is shown in the examples.
top^ or pow | power function, e.g. x^2 or pow(x#2) for x^{2}. A root can be written as power of a fraction, e.g. x^(1/2) or x^.5 for square root of x, an exponential function like this: e^x for e^{x}. Roots of negative values can only be shown, if the numerator 1 and the denominator is odd (e.g. x^(1/3) ). To calculate negative x-values for e.g. x^(2/3) , you have to alter this function into (x^(1/3))^2 |
sqr | square root, e.g. sqr(x) as equivalent to x^(1/2). |
exp | exponential function, Euler-function, e.g. exp(x) as equivalent to e^x. |
log | natural logarithm (logarithm to base e) , e.g. log(x) |
log10 | decadic logarithm, e.g. log10(x) |
logn | logarithm to base n, e.g. logn(2#x) for the binary (base 2) logarithm. |
sin | Sine, sinus, e.g. sin(x) |
cos | Cosine, cosinus, e.g. cos(x) |
tan | Tangent, e.g. tan(x) |
cot | Cotangent, e.g. cot(x) |
sin2 | Sine square, e.g. sin2(x) |
cos2 | Cosine square, e.g. cos2(x) |
tan2 | Tangent square, e.g. tan2(x) |
cot2 | Cotangent square, e.g. cot2(x) |
arcsin | Arcsine, e.g. arcsin(x) |
arccos | Arccosine, e.g. arccos(x) |
arctan | Arctangent, e.g. arctan(x) |
arccot | Arccotangent, e.g. arccot(x) |
sinh | Hyperbolic Sine, e.g. sinh(x) |
cosh | Hyperbolic Cosine, e.g. cosh(x) |
tanh | Hyperbolic Tangent, e.g. tanh(x) |
coth | Hyperbolic Cotangent, e.g. coth(x) |
arsinh | Area Hyperbolic Sine, e.g. arsinh(x) |
arcosh | Area Hyperbolic Cosine, e.g. arcosh(x) |
artanh | Area Hyperbolic Tangent, e.g. artanh(x) |
arcoth | Area Hyperbolic Cotangent, e.g. arcoth(x) |
sec | Secant, e.g. sec(x) |
cosec | Cosecant, e.g. cosec(x) |
arcsec | Arcsecant, e.g. arcsec(x) |
arccosec | Arccosecant, e.g. arccosec(x) |
sech | Hyperbolic Secant, e.g. sech(x) |
cosech | Hyperbolic Cosecant, e.g. cosech(x) |
arsech | Area Hyperbolic Secant, e.g. arsech(x) |
arcosech | Area Hyperbolic Cosecant, e.g. arcosech(x) |
cat | Catenary, e.g. cat(2#x) for 2*cosh(x/2). The first value is the constant a. |
gd | Gudermannian function, e.g. gd(x) for arctan(sinh(x)). |
siv | Semiversus, e.g. siv(x) for sin2(x/2). |
sinc | Sine cardinalis, e.g. sinc(x) for sin(x)/x. |
tanc | Tanc function or tangent cardinalis, e.g. tanc(x) for tan(x)/x. |
hubb | Hubbert curve, e.g. hubb(x) for 1/(2+2*cosh(x)). |
L | Langevin function, e.g. L(x) for coth(x)-1/x. |
deg | converts a radian number to the equivalent number in degrees, e.g. deg(pi) |
rad | converts a number in degrees to the radian equivalent, e.g. rad(180) |
abs | absolute value, e.g. abs(x) |
min | minimum of several values, e.g. min(1#x#x^(1/3)) as minimum of 1, x and third root of x. |
max | maximum of several values, e.g. max(abs(x)#x*x) as maximum of the absolute value of x and x^{2}. |
% | modulo division, whole-numbered remainder, e.g. 10%x |
fmod | modulo division, floating point remainder, e.g. fmod(x#1) displays only the position after the decimal point of the input value. |
R | round, e.g. R(x#2) rounds two decimal places, R(x) rounds to an integer. |
R0 | floor (rounding down), e.g. R0(x). This is equivalent to Gaussian brackets [x]. |
R1 | ceil (rounding up), e.g. R1(x) |
dist | distance function, e.g. dist(x) gives the distance to the nearest integer. |
prime | prime number function, e.g. prime(x) This returns the next lower prime number (or x itself, if prime) for all x≥2 and x≤100000. At all four prime functions, non-integers are rounded. |
prime1 | prime number detecting function, e.g. prime1(x) displays the number x only if x is prime, 0 otherwise. To find all prime numbers in an interval, the span of the x-axis shouldn't be wider than the width of the image (usually 500) and you should switch off poles. |
prime2 | distinct prime factor counting function, e.g. prime2(x) returns the amount of different prime factors for an integer. |
prime3 | prime factor counting function, e.g. prime3(x) returns the amount of prime factors for an integer, including multiples. E.g. prime2(4) = 1, whereas prime3(4) = 2. If prime3(x) = 1, then x is prime. |
div | divisor function, e.g. div(x) returns the number of divisors of an integer. Non-integers are rounded. |
dig | digit sum, e.g. dig(x) returns the digital sum of an integer. Non-integers are rounded, - is ignored. |
dig2 | iterated (one-digit) digit sum, e.g. dig2(x) returns the iterated digital sum of an integer. |
adig | alternating digit sum, e.g. adig(x) Non-integers are rounded, - is ignored. |
fac | factorial, e.g. fac(x) Non-integers are rounded. |
H | Heaviside step function, e.g. H(x) 0, if x≤0, else 1. |
Hm | multivariate Heaviside step function, e.g. Hm(x*x-1#sin(x)) 0, if at least one value ≤0, else 1. Enter as many arguments as you want. |
sig | signum function (sign function), e.g. sig(x) |
haar | Haar wavelet, e.g. haar(x) |
gcf | greatest common factor (or greatest common divisor, gcd), e.g. gcf(8#x) returns the greatest common factor between two integers. Non-integers are rounded. |
lcm | least common multiple, e.g. lcm(8#x) returns the least common multiple between two integers. Non-integers are rounded. |
mo | Möbius function, e.g. mo(x) returns for all positive integers 0, if divisible by a square>1, -1 if it has an odd number of distinct prime factors and 1 if it has an even number of distinct prime factors. Non-integers are rounded. Values are allowed up to 100000. |
toti | Euler's totient function, e.g. toti(x) counts all positive integers less than x that are comprime to x. Non-integers are rounded. |
odd | find odd numbers, e.g. odd(x) returns numbers only when odd. Non-integers are rounded. |
even | find even numbers, e.g. even(x) returns numbers only when even. Non-integers are rounded. |
bin | binomial coefficient, e.g. bin(4#x) The two values are n and k. Non-integers are rounded. |
tri | triangle curve, e.g. tri(1#2#x) The first value is the period, the second is the amplitude. |
rect | rectangle curve, e.g. rect(1#-1#2#x) The first value is the upper limit, the second is the lower and the third is the period. |
saw | sawtooth wave, e.g. saw(2#1#x) The first value is the period, the second is the amplitude. |
saw2 | reverse sawtooth wave, e.g. saw2(2#1#x) The first value is the period, the second is the amplitude. |
ramp | ramp function, e.g. ramp(1#2#1#x) The first value is the start value, the second is the end value and the third is the height. |
ramp2 | reverse ramp function, e.g. ramp2(1#2#1#x) The first value is the start value, the second is the end value and the third is the height. |
trap | trapezium (trapezoid) function, e.g. trap(-4#-1#3#2#3#x) The first value is the start value of the climb, the second is the end value of the climb, the third is the height, the fourth is the start value of the descent and the fifth is the end value of the descent. |
poly | polygon or chart line, e.g. poly(-4#2#-3#4#-2#1#-1#0#0#3#1#2#2#-1#3#3#4#1#x) gives a chart, respectively a half polygon. Here, (-4,2) is connected to (-3,4), this to (-2,1) and so on. The first value of each pair is the x-value, the second one is the y-value. The x-values must increase with each step. To get a full polygon, enter a second term with the same start and end points, like poly(-4#2#0.5#-4#4#1#x) |
rand | integer random number between two integers, e.g. rand(0#2) returns 0, 1 or 2 (Mersenne twister is used for generating). |
rand2 | random number between two numbers with decimal places (maximal 9), e.g. rand2(0#1#3) returns a number with three decimal places between 0 and 1 (Mersenne twister, too). |
norm | normal or Gaussian distribution, e.g. norm(2#1#x) for the standard normal Distribution shifted two Units to the right. The first value is the expected value, the second is the standard deviation. |
phi | Φ, cumulative Gaussian distribution function, e.g. phi(0#1#x) This is an approximation based on the displayed interval. It delivers reasonable values, if the normal distribution in the chosen interval starts at very low values near 0. A common display of both functions is advisable. |
chi2 | chi-square distribution, e.g. chi2(3#x) The first value is the number of the degrees of freedom. |
ichi2 | inverse-chi-square distribution, e.g. ichi2(3#x) The first value is the number of the degrees of freedom. |
sichi2 | scale-inverse-chi-square distribution, e.g. sichi2(3#1#x) The first value is the number of the degrees of freedom, the second is the scale parameter, both must be >0. |
chi | chi distribution, e.g. chi(3#x) The first value is the number of the degrees of freedom. |
stud | Student's t-distribution (also known as t-distribution), e.g. stud(2#x) The first value is the number of the degrees of freedom. |
F | F-distribution (Fisher-Snedecor), e.g. F(5#2#x) The first two values are the numbers of the degrees of freedom. |
Fz | Fisher's z-distribution, e.g. Fz(5#2#x) The first two values are the numbers of the degrees of freedom. |
lnorm | log-normal distribution, e.g. lnorm(0#1#x) The first value is the mean, the second is the standard deviation. |
cau | Cauchy distribution or Lorentz distribution, e.g. cau(0#1#x) for the standard Cauchy distribution. The first value is the location parameter, the second is the scale parameter. |
lapc | Laplace distribution, e.g. lapc(0#1#x) The first value is the location parameter, the second is the scale parameter. The second parameter must be >0. |
logd | logistic distribution, e.g. logd(1#2#x) The first value is the location parameter, the second is the scale parameter. |
hlogd | half-logistic distribution, e.g. hlogd(x) |
rlng | Erlang distribution, e.g. rlng(5#1#x) The first value is the shape parameter, the second is the rate parameter. The first parameter must be a natural number. |
pon | exponential distribution, e.g. pon(1#x) The first value is the rate parameter. |
cosd | raised cosine distribution, e.g. cosd(0#1#x) The first value is the location parameter, the second is the scale parameter. cosd is defined in the interval [location-scale;location+scale]. |
sechd | hyperbolic secant distribution, e.g. sechd(x) |
kum | Kumaraswamy distribution, e.g. kum(2#3#x) The first two values are the shape parameters a and b. |
levy | Lévy distribution, e.g. levy(1#x) The first value is the scale parameter. |
rlgh | Rayleigh distribution, e.g. rlgh(1#x) The first value is the scale parameter. |
wb | Weibull distribution, e.g. wb(2#1#x) The first value is the shape parameter, the second is the scale parameter. |
wig | Wigner semicircle distribution, e.g. wig(1#x) The first value gives the radius. |
gammad | gamma distribution, e.g. gammad(2#3#x) The first value is the shape parameter, the second is the scale parameter. |
igammad | inverse-gamma distribution, e.g. igammad(2#1#x) The first value is the shape parameter, the second is the scale parameter. |
igauss | inverse Gaussian distribution, e.g. igauss(1#0.25#x) The first value is the shape parameter, the second is the scale parameter. |
betad | beta distribution, e.g. betad(2#3#x) The first two values are the shape parameters, these must be ≥0. betad is defined for x in [0;1]. |
betap | beta prime distribution, e.g. betap(2#3#x) The first two values are the shape parameters, these must be >0. |
par | Pareto distribution, e.g. par(2#1#x) The first value is the location parameter, the second is the shape parameter. |
pear | Pearson distribution (type III), e.g. pear(1#1#2#x) The first value is the location parameter, the second is the scale parameter and the third is the shape parameter. |
nak | Nakagami distribution, e.g. nak(4#1#x) The first value is the shape parameter, the second is the spread parameter. |
shg | shifted Gompertz distribution, e.g. shg(0.5#1#x) The first value is the scale parameter, the second is the shape parameter, both must be >0. |
brw | relativistic Breit-Wigner distribution, e.g. brw(1#2#x) The first value is the mass of the resonance, the second is the resonance's width and the third is the energy. |
gen | generalized extreme value distribution, e.g. gen(0#1#0.2#x) The first value is the location parameter, the second is the scale parameter and the third is the shape parameter. |
Ft | Fisher-Tippett distribution, e.g. Ft(1#2#x) The first value is the location parameter, the second is the scale parameter. The second parameter must be >0. |
rossi | Rossi distribution, or mixed extreme value distribution, e.g. rossi(0#3#1#4#x) The first four values are c1, c2, d1 and d2. |
gum1 | Gumbel distribution type 1, e.g. gum1(2#1#x) The first two values are the parameters a and b. |
gum2 | Gumbel distribution type 2, e.g. gum2(2#1#x) The first two values are the parameters a and b. |
trid | triangular distribution, e.g. trid(1#2#4#x) The first value is the lower limit, the second is the most probable and the third is the upper limit. |
bind | Binomial distribution, e.g. bind(5#0.4#x) The first value is the number of trials, the second is the success probability. |
nbin | Negative binomial distribution, e.g. nbin(3#0.4#x) The first value is a paremater >0, the second is a probability. |
poi | Poisson distribution, e.g. poi(3#x) The first value is λ, the second is the expected value. |
skel | Skellam distribution, e.g. skel(1#2#x) The first two values are the means of two different Poisson distributions. |
gk | Gauss-Kuzmin distribution, e.g. gk(x) |
geo | Geometric distribution (variant A), e.g. geo(0.8#x) The first value is a probability. |
hgeo | Hypergeometric distribution, e.g. hgeo(8#3#2#x) The first value is the total number of objects, the second is the total number of defective objects, the third is is the number of sample objects and the fourth the number of defective objects in the sample. |
yule | Yule-Simon distribution, e.g. yule(2#x) The first value is the shape parameter. |
logs | Logarithmic series distribution, e.g. logs(0.1#x) The first value is a probability. |
zipf | Zipf or zeta distribution, e.g. zipf(3#x) The first value is a parameter >0. |
zm | Zipf-Mandelbrot law or Pareto-Zipf law, e.g. zm(100#1#2#x) The first three values are N, q and s. Maximum for N is 100. |
uni | Uniform distribution, e.g. uni(1#2#x) The first value is the lower limit, the second is the upper limit. |
traj | Trajectory parabola, path of a thrown object, e.g. traj(45#20#9.81#x) The first value is the angle, the second is the speed (e.g. in meters per second). The third value is the gravitational acceleration (e.g. in m/s²), the normal value on earth for this is g = 9.81 m/s². The axes scale in this example is meters. Air resistance is ignored. |
pll | Parallel operator, as used, among others, for the calculation of parallel circuits and resistances, e.g. pll(20#30#x) Enter as many arguments as you want. |
M1 | Arithmetic mean, e.g. M1(2#3#x) Enter as many arguments as you want. |
M2 | Geometric mean, e.g. M2(2#3#x) Enter as many arguments as you want, only positive values are allowed. |
M3 | Harmonic mean, e.g. M3(2#3#x) Enter as many arguments as you want, only positive values are allowed. |
M4 | Root mean square, e.g. M4(2#3#x) Enter as many arguments as you want. |
M5 | Median, e.g. M5(2#3#x) Enter as many arguments as you want. |
scir | Semicircle curve, e.g. scir(x#1) for a semicircle with the radius 1. The formula is sqr(r*r-x*x), r gives the radius. |
ell | Semielliptic curve, e.g. ell(2#1#x) for a semiellipse with the horizontal radius 2 and the vertical radius 1. The formula is sqr((1-x*x/(a*a))*b*b). |
ell2 | Semi-superellipse or semi-hyperellipse, e.g. ell2(2#3#4#x) for a semiellipse with the horizontal radius 2, the vertical radius 3 and n=4. |
lmn | Lemniscate of Bernoulli, e.g. lmn(1#x) This returns a half lemniscate. For the other half, use -lmn(1#x) |
lmn2 | Lemniscate of Gerono, e.g. lmn2(x) This returns a half lemniscate. For the other half, use -lmn2(x) |
lmn3 | Lemniscate of Booth, e.g. lmn3(1#x) This returns a half lemniscate. For the other half, use -lmn3(1#x) |
pyth | Pythagorean theorem, e.g. pyth(x#1) The formula is c=sqr(a*a+b*b). |
thr | Rule of three, e.g. thr(x#1#2) The formula for thr(a#b#c) is f(x)=b*c/a. |
fib | Fibonacci numbers, e.g. fib(x) or fib(x#1) If the second value is 1, a continuous graph is shown, else a discrete. |
dc | Exponential decay, e.g. dc(5#1#x) The first value is the initial quantity, the second is the decay constant. |
erf | Gaussian error function, e.g. erf(x) For the computation its Taylor series is used. |
HY4 | Hyper4, also known as tetration or super-exponentiation, e.g. HY4(x#3) for x to the power of (x to the power of x). Here the maximum value can be excessed very quickly! |
lambda | Lambda function, e.g. lambda(x#3) for x to the power of (x to the power of (3-1)). |
sgm | Sigmoid function, e.g. sgm(x) for 1/(1+e^(-x)). |
gom | Gompertz curve, e.g. gom(2#-5#-3#x) The first value is the upper asymptote, the second is the parameter b and the third is the growth rate. Second and third value must be negative. |
zeta | Riemann zeta function for values >1, e.g. zeta(x) |
eta | Dirichlet eta function, e.g. eta(x) |
stir | Stirling's approximation for large factorials, e.g. stir(x) The formula is (2*pi*x)^(1/2)*(x/e)^x. |
gamma | Gamma function (Euler and Weierstrass definition, approximation), e.g. gamma(x) as extension of the factorial function and for many statistical distributions. |
beta | Euler beta function, e.g. beta(2#x) |
digamma | Digamma function, e.g. digamma(x) for D(gamma(x))/gamma(x). |
omega | Lambert-W function or Omega function or product log (approximation), e.g. omega(x) |
theta | Ramanujan theta function, e.g. theta(x#0.3) The two values are a and b. abs(a*b) must be <1. |
bump | Bump function psi, ψ, e.g. bump(x) for exp(-1/(1-x*x)) between -1 and 1, else 0. |
srp | Serpentine curve, e.g. srp(2#1#x) The formula is a*a*x/(x*x+a*b). The first two values are a and b. |
bsc | Gaussian bell-shaped curve, e.g. bsc(1#x) The formula is exp(-a*a*x*x), the first value is the shape parameter a. |
gbsc | Generalized Gaussian bell-shaped curve, e.g. gbsc(1#2#-1#x) for 1*exp(2*x-1*x*x). |
bool | Characteristic boolean function, e.g. bool(1/x) Returns nothing, if the input value is not defined, 0, if 0, else 1. | |
bool0 | Defined boolean function, e.g. bool0(x) Returns 0, if the input value is 0 or not defined, else 1. | |
bool1 | Undefined boolean function, e.g. bool1(prime1(x)) Returns nothing, if the input value is 0 or not defined, else 1. | |
con | Condition function, e.g. con(0#sin(x)#1) The first value is the lower limit, the third is the upper limit. If the second value is between these two, the result is 1, else 0. | |
rcon | Reverse condition function, e.g. rcon(0#sin(x)#1) The first value is the lower limit, the third is the upper limit. If the second value is between these two, the result is 0, else 1. | |
wcon | Weighted condition function, e.g. wcon(0#sin(x)#1) Only returns the second value, if this lies between the first and the third value. | |
rwcon | Reverse weighted condition function, e.g. rwcon(0#sin(x)#1) Only returns the second value, if this doesn't lie between the first and the third value. | |
&& (and) | can be simulated with the minimum function, e.g. min{ con[0#sin(x)#1] # con[0#cos(x)#1] } | |
|| (or) | can be simulated with the maximum function, e.g. max{ con[0#sin(x)#1] # con[0#cos(x)#1] } | |
⊕ (xor) | can be simulated with the maximum minus the minimum function, e.g. max{ con[0#sin(x)#1] # con[0#cos(x)#1] } - min{ con[0#sin(x)#1] # con[0#cos(x)#1] } |
Attention: derivative and integral with the iteration don't lead to very reasonable results. As well a logarithmic scale won't work here.
y | Previous function value, e.g. for y(0)+0.01 is 0 the initial value for y, the next value is the last result of the input value x and so on. |
y2 | Pre-previous function value, e.g. y2(1)+0.001 |
step | Number of the iteration steps done, divided by the parameter value, e.g. step(100) counts up to five (at 500 px width). |
mean | Iterated arithmetic mean, e.g. mean(sin(x)) gives the arithmetic mean of function values calculated from the leftmost up to the current value in x. |
man | Mandelbrot function, e.g. man(0#-1.9) for y(0)*y(0)-1.9. |
rsf | Random singular function (a kind of devil's staircase), e.g. rsf(0#2) for y(a)+0.008*rand(0#1)*rand(0#1)*(b-a), from a (first value) to b (second value) at 500px width. The first value is the start point on the y-axis, the second is the average end value. |
wf | Weierstrass function, e.g. wf(x#0.5#17#10) The second value is a parameter between 0 and 1, the third value is a positive, odd integer. The second multiplied with the third must be larger than 1+3/2*pi. The fourth value is the number of steps done. In theory this is infinite, but here the maximum is 100. |
blanc | Blancmange curve, e.g. blanc(x#10) The second value is the number of steps done, maximum is 1000. |
tak | Takagi-Landsberg curve, e.g. tak(x#0.7#10) The second value is a parameter, which should be between 0 and 1. The third is the number of steps done, maximum is 1000. |
D or D1 First derivative, e.g. D(x*x) D2 Second derivative, e.g. D2(x^3) D3 Third derivative, e.g. D3(x^4) |
D0 or D01 First derivative, alternative form, e.g. D0(x*x) D02 Second derivative, alternative form, e.g. D02(x^3) D03 Third derivative, alternative form, e.g. D03(x^4) |
S or S1 first integral, e.g. S(x*x) S2 second integral, e.g. S2(x) S3 third integral, e.g. S3(1) |
image type: | plotter knows three image formats: png (compression level 1), gif (GIF87a) or jpeg (90 percent quality level). The jpeg image format does not Support transparency. |
width / height | set the size of the image in pixels. For practical reasons, minimum size is 200, maximum is 500. |
range | defines the interval the curves are displayed in. Maximal input and output value is 100000 (or -100000). With a logarithmic scale, the output value can raise up to about 10^{300}. Constants like pi are allowed, too. |
intervals | number of sectors on each axis labeled with dashes and numbers. Maximum is 250 or half of the width / height. |
grid lines | the number of the drawn lines in the grid. Maximum is half of the width or height. |
dashes length | length of the dashes at interval borders. Maximum length is 500. |
decimal places | defines the number of decimal places displayed. This is used for calculation of values, too. Maximum is 12. |
gap at origin | sets the size of an optional gap around the origin. If set to 0, no gap is shown. |
graph thickness | line thickness of function graphs. Values can be positive integers up to 200 (which looks quite funny...). |
log. scale | select linear or logarithmic scale on one or both axes. If no logarithm is selected, an axis will be drawn using a linear scale. You can choose 2, e, 10 or 100 as logarithmic base or enter an individual value. Caution: logarithmic display will not work in combination with integrals, derivates or iterations. |
quadrants | offers buttons to change the displayed quadrants and an input field for their size. If you wish to change the size, do so before clicking one of these buttons. |
To calculate values, you need a function in the syntax used for plotter input already (see above). There are three buttons that will copy the function definitions in the plotting part (named f(x), g(x) and h(x)).
Variable values used to calculate distinct points on the curve can be given in text form (a line of numbers separated by spaces), the buttons +10/-10 will enter whole numbers from 1 to 10 rsp -1 to -10.
Once calculated, the values will be displayed in the Format selected by the radio buttons - a line of numbers, table, in csv-notation (semicolon-separated) or as a snippet of Latex code.
Each time a plot is created, all selected values and options are concatenated into a (long!) query string to pass the relevant data to the graphing part and get the actual image. The plot can be redrawn anytime by passing this data to graph.php (which will return an image in the previously selected format). All the required information is stored in the query string - so the URL displayed in the text field can be used to create a predefined plot on the fly, there's no need to save the image into a file. Of course, the URL can be saved as text to create a plot later on.
Direct linking to a function plot is a nice feature, but the URL with plotter's options is really ugly. That's why there's a short link (tinyurl-a-like) in the upper field. This one can be used if you do not need a direct link to the image (if a redirection is acceptable).
By appending " .qr " to the end of the short link, you'll get a QRCode (as a png image) of the short link which in turn will redirect to the image of the created plot - simple, huh?
All images created by the plotter located at plot.oettinger-physics.de are covered by a WTFPL-License or in other words, they are released into public domain. Please do not use the plotter if you don't feel comfortable with this.
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