Infinite Mystery Curves II: Parametric Curves Built from Sum and Integral Concep

This example demonstrates how “Infinite Mystery Curves II” can be generated dynamically by iterating parameters and accumulating terms to reveal structured curve shapes. It connects several core ideas: parametric curve graphing, relationships between functions (including linear components), geometric-mean style quantities that set the scale of combined expressions, Poisson-distribution-like weighting through probability parameters, and the use of definite-integral/summation viewpoints to model accumulated effects. Construction-wise, the key workflow is to use GeoGebra’s Sum command to compute a running total over indexed terms (with n acting as the iteration index) and then map the resulting expressions to the plane using CurveCartesian to draw the Cartesian graph. The design relies on variables and objects such as parameters (n, h, speed, p), computed function outputs (f, val, c), and navigation/iteration controls (button1/button2/button3, NextLr/NextLexp/NextLt) to update the curve step-by-step; additional objects like MistRe and MistIm support the visualization of real/imaginary-like components in the constructed quantity. Suitable for high school to early university use in graphing, calculus intuition via accumulation, and introductory probability/statistics applications (Poisson), as well as for learners practicing parameterized modeling and numerical summation.