Many triangle centers, as listed in ETC, offer links to sketches of various types.
Some of them are described here.
These dynamic sketches can be opened by GeoGebra Classic 6. A free download of this highly recommended resource for creating, experimenting, and discovering, is available at THIS SITE. (There are several options; be sure to choose GeoGebra Classic 6.)
Examples of ggb sketchs in ETC: X(1)-X(29) and many others.
These sketches can be opened by The Geometer's Sketchpad. Although this program was discontinued in 2020, GSP sketches have been retained in ETC for users who have this software.
Examples of gsp sketchs in ETC: X(1)-X(29) and many others.
These are easy-to manage non-dynamic sketches - just click. Examples in EXP:
X(3): Ellipse associated with the circumcenter
X(3): Hyperbola associated with the circumcenter
X(20): "Pythagorean snail"
X(57): A construction involving the intouch triangle
X(33602): A construction involving equilateral triangles
X(50032): 1st Miyamoto-Lozada center
There are non-dynamic sketches hosted by geogebra.org.
Example used at X(33602): Generalization of the first Fermat-Dao-Nhi equilateral triangle
X(3): Extremal Area Pedal and Antipedal Triangles
X(6): Suprisingly Stationary Symmedian Point of the Inversive Image of an X(6)-Pivoting Triangle
X(9): N = 3 orbits in elliptic billiard: Anticomplementary triangle intouch points and circumbilliard
X(13): 3-Periodics in a Concentric Homothetic Poncelet Pair: Circular Loci of Four Triangle Centers
X(13): Loci of Centers of Ellipse-Mounted Triangles
X(15): Experiment: Isodynamic Points IV: flank triangles between hexagons erected on a triangle's sides have common X16
X(39): It takes 2 to tango: Brocard-Poncelet Porism, stationary Brocard Points and invariant Brocard Angle
X(39): Joined at the hip: Brocard Porism, Steiner Ellipses, and the Homothetic Poncelet Pair
X(39): The Poncelet Homothetic Pair contains an Aspect-Ratio Invariant Brocard Inellipse
X(88) and X(162): Dance of the Swans: X(88) and X(162) and their Never-Touching Motion Over the Elliptic Billiard
Many websites include sketches of triangles with triangle centers. A selection follows:
Wikipedia: "Triangle Center" (includes links to sketches)
Wikipedia: "Modern triangle geometry" (includes links to sketches)
MathWorld: "Incenter" (includes links to sketches)
MathWorld: "Kimberling Center" (includes links to sketches)
Cubics in the Triangle Plane, Bernard Gibert's site, with thousands of intricate sketches involving triangle centers and associated curves. See, for example, K001: Neuberg cubic