Julia Set Viewer
Julia sets are like snapshots of the Mandelbrot set at a specific point.
Drag the image above to select where the point is
located (the white circle). The Julia set is drawn in real-time using the GPU, and will smoothly change as you adjust the point.
Both fractals are created by the same iterated equation Z = Z2 + C, but in Julia sets,
C is the selected point and is constant for every pixel. The pixel position
is the initial value of Z. This produces a fractal consisting only of the specific style
of swirls in the Mandelbrot set near that point. If the point is inside the Mandelbrot set, then the Julia set is connected.
Otherwise, it is a dust of infinitely many disconnected pieces. Zoom in on the Mandelbrot set image if you want more
precision in positioning the point. The power value changes the exponent of Z in the equation. The inverse option
takes the complex inversion on the Riemann sphere (the reciprocal) of the function domain. The current point will automatically be moved
to the inverse point when the option is turned on or off.
Julia sets can be defined for the Burning Ship fractal in the same way as for the Mandelbrot set. The equation is identical, except it takes the absolute value of the components before the exponentiation: Z = (|Re(Z)| - i|Im(Z)|)2 + C
The mode specifies how the coloring is calculated. For escape time, it counts the number of iterations before Z diverges toward infinity. For the minimum point mode, it keeps track of the Z value with the smallest magnitude seen out of all iterations, and then replaces the final Z with it. (All iterations are computed for every pixel, so this mode is significantly slower.) This is useful for negative fractal powers, since the escape time is an inaccurate measurement. Points that diverge will alternate between increasingly large and small values, because a negative power is equivalent to division by a positive power. However, any value that remains bounded must remain larger than a constant magnitude (otherwise it would explode toward infinity on the next iteration), so the point with minimum magnitude will be non-zero if and only if it's inside the fractal set. (To match the aesthetics of the divergence coloring, it takes the reciprocal of the min point to make the inside glow while the outside is dark.)
Julia sets can be defined for the Burning Ship fractal in the same way as for the Mandelbrot set. The equation is identical, except it takes the absolute value of the components before the exponentiation: Z = (|Re(Z)| - i|Im(Z)|)2 + C
The mode specifies how the coloring is calculated. For escape time, it counts the number of iterations before Z diverges toward infinity. For the minimum point mode, it keeps track of the Z value with the smallest magnitude seen out of all iterations, and then replaces the final Z with it. (All iterations are computed for every pixel, so this mode is significantly slower.) This is useful for negative fractal powers, since the escape time is an inaccurate measurement. Points that diverge will alternate between increasingly large and small values, because a negative power is equivalent to division by a positive power. However, any value that remains bounded must remain larger than a constant magnitude (otherwise it would explode toward infinity on the next iteration), so the point with minimum magnitude will be non-zero if and only if it's inside the fractal set. (To match the aesthetics of the divergence coloring, it takes the reciprocal of the min point to make the inside glow while the outside is dark.)