Lazarus/Free Pascal curlicue fractal.
| Download CurlicueFractal desktop application (Windows 64bit) | Download CurlicueFractal source code (Lazarus/Free Pascal) |
Description: The curlicue fractal is generated by starting with a line segment of unit length and adding to it subsequent line
segments of the same length, but different angles. These angles are given by the series ϕ[n+1] = (ϕ[n] + θ[n]) % 2π, with ϕ[0] = 0. θ[n+1] is given by
θ[n+1] = (θ[n] + 2πs) % 2π, with θ[0] = 0 (% being the "modulo" operator). The value of s has to be an irrational number (at least to get interesting fractals).
"CurlicueFractal" is a Lazarus/Free Pascal PC application that may be used to draw such fractals. The value of s may be chosen from some typical examples of
irrational numbers: π, ϕ (golden ratio), √2, ln(2), e, γ (Euler-Mascheroni constant), δ (Feigenbaum constant), and some others, or entered by the user.
The user can also choose the number of curve points to be calculated and the length of the line that is added during each iteration. Finally, there are four
direction buttons that allow to adapt the position of the fractal on the drawing surface.
Extension: Would be nice to give the user the possibility to print out the fractal drawing, or to save it as PDF file.
Free Pascal features: Graphics, drawings, bitmaps, canvas drawing, drawing of mathematical curves. Adaption of the position of a curve on
the drawing surface using positioning buttons.
Screenshot:
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