features.md

Features & Guide

This document is an exhaustive list of features implemented and non-exhaustive guide on how to use it.

2D Plotting

Plots complex functions $f:\mathbb{C} \to \mathbb{C}$ with standard domain coloring. This mode allows for user interactions to explore the graph, such as:

• Panning: Click and drag to pan around the function's plot.
• Zooming: Use the scroll wheel to zoom. Has high precision up to 10^{-8}
• Hovering: Hovering with a cursor over a point will show the input value $z$ and its output $f(z)$

3D Plotting

Plots complex functions using a domain coloring map, and also a height map, where the height is mapped as $h = |f(z)|$. Allows for panning and zooming as well as:

• Moving: WASD keys to move around the function plot. Shift to go up, Ctrl to go down.
• Rotating: Right mouse + Drag to rotate your camera.

Function Parser

The plotter includes a custom recursive descent parser that supports complex-valued expressions.

Syntax rules

• Variables: Supports z (the input variable), x (real component), y (imaginary component) and t (time passed)
• Constants: All numeric constants, i (the imaginary unit), pi and e (euler's number)
• Implicit multiplication: Expressions such as 2z or 2(z+2) will be evaluated as 2*z and 2*(z+2)

Supported functions

This plotter supports every elementary function. The full list of supported functions is automatically updated as new ones are added, so always make sure to double check on the app's "Help & Keybinds" section. The full list, as of now, of supported functions is:

Category	Functions
Arithmetic	+, -, *, /, ^ (power), % (modulo)
Exponential	exp ($e^z$), log (natural), sqrt
Trigonometry	sin, cos, tan, sec, csc, cot
Inverse Trig	asin, acos, atan, asec, acsc, acot
Hyperbolic	sinh, cosh, tanh, sech, csch, coth
Inverse Hyperbolic	asinh, acosh, atanh, asech, acsch, acoth
Complex Structure	abs (Modulus), arg (Phase), real, imag, conj

Derivatives

This plotter supports symbolic differentiation! This means that an expression like $\frac{d}{dz}(z^2 + \sin(z))$ will be evaluated as $2z + \cos(z)$ All derivatives are assumed to be in the form $\frac{d}{dz}$, and should be written as derivative(expression).

Render Modes

This plotter offerts two backend modes for evaluating functions: Interpreted and Compiled. By default, they are automatically applied to their best usecase, this may be changed in the settings.

Interpreted Mode

Interpreted Mode has instant updates, but becomes slower for large expressions. By default, as you type, it updates the graph immediately.

Compiled Mode

Compiled Mode has higher speed, but requires a slightly larger time to be ready than Interpreted Mode. You can activate this by pressing the enter key, or compile button.

Grid

Allows for a grid mapped to input (serves as a reference to where the components of $z$ are integers), and to output (shows how $f(z)$ warps the function space).

Animations

Time is a supported variable, t. Modulo and trigonometric operators are supported, so it is possible to do animations with expressions like z^(sin(0.5t)*10) (bounce) or z^((t % 10) * 10) (repeat). Try some of these!

• z * exp(i * t)
• sin(z + t)
• (1-sin(t))*z + sin(t)*z^2
• tan(z)^(sin(t)) % sin(z)

Ultra high precision mode

Plots can be rendered in arbitrary precision through the "Arbitrary Precision" subheader. This means that functions will be rendered up to a user-defined value of decimal digits, which defaults to 50. This is particularly useful for seeing fractal-like functions in high zoom values