I am a retired math prof. I've worked with high school honor students as a mentor. I've found Peitgen's book on Chaos to contain a very comprehensive amount of material and to be written so well that students for sophomore high school to college graduate level get a lot from the articles. Chaos encompasses so much of classical mathematics as well as new ideas which have originated in the last 30 years that it is a really fun way to enrich the math curriculum without simply trying to push students more rapidly through standard material. Peitgen has prepared a few high school guides as well but I do not have a reference.
One of my students scanned leaves and computed the fractal dimensions of their edges. Using this data she developed and analyzed a classification scheme across both individual trees and species.
Her efforts earned her three firsts (math, computer science and biology) in the International Science Fair.
Hope this helps.
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I am a retired math prof. I've worked with high school honor students as a mentor. I've found Peitgen's book on Chaos to contain a very comprehensive amount of material and to be written so well that students for sophomore high school to college graduate level get a lot from the articles. Chaos encompasses so much of classical mathematics as well as new ideas which have originated in the last 30 years that it is a really fun way to enrich the math curriculum without simply trying to push students more rapidly through standard material. Peitgen has prepared a few high school guides as well but I do not have a reference. One of my students scanned leaves and computed the fractal dimensions of their edges. Using this data she developed and analyzed a classification scheme across both individual trees and species. Her efforts earned her three firsts (math, computer science and biology) in the International Science Fair. Hope this helps.