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Julia Trek App JULIA TREK Julia Trek Go To App Store


JuliaTrek is an app that lets you explore 24 curated fractal types:

  1. Mandelbrot
  2. Cubic Mandelbrot
  3. Quadric Mandelbrot
  4. Quintic Mandelbrot
  5. Perpendicular Mandelbrot
  6. Burning Ship
  7. Bird Of Prey
  8. Buffalo
  9. Celtic
  10. Druid
  11. Tricorn
  12. Cubic Tricorn

along with their 12 Julia counterparts.

  1. Julia
  2. Julia Cubic Mandelbrot
  3. Julia Quadric Mandelbrot
  4. Julia Quintic Mandelbrot
  5. Julia Perpendicular Mandelbrot
  6. Julia Burning Ship
  7. Julia Bird Of Prey
  8. Julia Buffalo
  9. Julia Celtic
  10. Julia Druid
  11. Julia Tricorn
  12. Julia Cubic Tricorn

It uses a futuristic TNG GUI and lets you create amazingly beautiful, shallow-depth, quasi-3D fractals using the SAM (Stripe Average Method) gradient coloring. You can also use 'Smooth CPM' and 'Basic' coloring, enhanced with 'Density Controls' and 'Palette Roll' to color the fractals. JuliaTrek includes an awesome, innovative and extremely powerful Gradient Designer so that you can create your own custom gradients with an unlimited number of colors, which are used in all coloring methods.

Custom gradients can be stored in the Gradient Library for quick access, and fractals can be stored in the Fractal Library, complete with preview images so that you can conveniently find them visually later on. Batches of fractal presets and single fractal files can be stored to disk via the standard Save Panel.

Workflow is extremely optimized in this app. Smart autorendering allows you to quickly make successive parameter changes to your fractal without having to wait for each change to render. In other words, if you have autorendering enabled, then every time you make a change to the fractal it will automatically abort the previous rendering and start rendering a new fractal with the new value.

Julia Fractals:

JuliaTrek employs a unique approach to exploring Julia fractals in two different ways. First, when in Julia-mode, you can click anywhere in the dynamically zoomable non-Julia fractal in the smaller fractal navigator view, which will automatically render a new Julia fractal in the larger fractal previewer using the click point as the new julia seed coordinate.

Alternatively, when in Standard-mode, you can click the 'JULIA ON/OFF' button (in the top bar) to toggle into Julia-mode, which automatically transfers the position and zoom of the standard fractal from the large main fractal viewer into the proto fractal in the small fractal navigator view and renders a new small proto fractal, and simultaneously, a new julia fractal is rendered in the large fractal viewer using a new julia seed based on the position of the standard fractal at the time of the toggle. The location of this new julia seed is shown by the white square targeter in the small fractal navigator. The upshot of this is, you are seeing the julia fractal that is located at the exact center of the previously shown standard fractal image.

You can export fractal images up to 4096x4096 pixels in size, and they are always rendered using 9x (3x3) supersampled antialiasing for stunning images.

JuliaTrek is multi-threaded, so you can export multiple fractals simultaneously, and still continue to explore new preview fractals at the same time.

Burning Ship and Bird Of Prey:

The Burning Ship and Bird Of Prey fractals are less famous than the Mandelbrot fractal, but are equally fractacular. What the Mandelbrot fractal does with spiral and curlicue patterns, the Burning Ship family of fractals does with lines, arcs, boxes, triangles, hearts, and other geometric shapes. Fantastic ship masts and sails, butterflies, insectoids, crescent moons, and a plethora of variations lurk in the depths, awaiting your discovery.

Perpendicular Mandelbrot:

The Perpendicular Mandelbrot fractal renders a 2D planar slice of the second order 3D Mandelbulb that is directly perpendicular to the Mandelbrot fractal.

Perpendicular Mandelbrot Fractal


The Druid fractal formula uses the standard Mandelbrot formula for even numbered iterations and the Celtic formula for odd iterations. There are a plethora of heart-shaped fractals to be found, such as the one used in the JuliaTrek icon and the following image, which is 2560 x 1440, and can be downloaded and used as a Desktop image or part of a screensaver collection.

Druid Fractal wallpaper


Fractal Formulas:

Mandelbrot: z^2 + c
Cubic Mandelbrot: z^3 + c
Quadric Mandelbrot: z^4 + c
Quintic Mandelbrot: z^5 + c
Perpendicular Mandelbrot: z^2 + c           where:
Zi = -2 * Zr * |Zi| + Ci
Zr = Zr * Zr - Zi * Zi + Cr
Burning Ship: z^2 + c           where:
Zi = 2 * |Zr * Zi| + Ci
Zr = Zr * Zr - Zi * Zi + Cr
Bird of Prey: z^3 + c           where:
Zi = ((Zr^2 * 3) - Zi^2) * |Zi| + Ci
Zr = (Zr^2 - (Zi^2 * 3)) * |Zr| + Cr
Buffalo: z^2 + c           where:
Zi = 2 * |Zr * Zi| + Ci
Zr = |Zr^2 - Zi^2| + Cr
Celtic: Z = Z - Zr + |Zr| + C
Druid: Even Iterations: Mandelbrot
Odd Iterations: Celtic
Tricorn: (conjugate(z))^2 + c
Cubic Tricorn: (conjugate(z))^3 + c

Fractal Orbit Path Visualization

This app has the ability to show the orbit path of a point in fractal space.

For a subset of fractal types – Mandelbrot, Cubic Mandelbrot, Quadric Mandelbrot, Quintic Mandelbrot, and Perpendicular Mandelbrot – you can observe the orbit points and follow their iteration path, in real time, by control dragging in the main fractal view. However, this only works when the zoom factor is an integer between 1 and 10 inclusive.

The orbit paths with the most interesting geometric patterns are found in the interior of the fractal set, but near the border. In some areas, such as in the centers of the bulbs, the orbit points become an infinitely repeating pattern. In the images below, the red circle within the large white circle marks the first point, and the white lines successively connect to the following points in the iteration sequence.

Mandelbrot Fractal Orbit Path

Mandelbrot Fractal Orbit Path

Mandelbrot Fractal Orbit Path



  • 24 Different Fractal Types
  • SAM (Stripe Average Method) Fractal Coloring
  • Smooth CPM (Continuous Potential Method) Fractal Coloring
  • Iteration/IterationMax Fractal Coloring
  • Gradient Density Controls
  • Gradient Palette Roll Controls
  • Multi-threaded
  • Multiple Simultaneous Fractal Image Export
  • Simultaneous Export and Fractal Preview Rendering
  • Awesome Gradient Designer
  • Unlimited Gradient Colors
  • Supersmooth gradient color interpolation
  • 3x3 Supersampled Antialiasing
  • Fractal Library
  • Gradient Library
  • Single-key Time-stamped Fractal Save to Desktop
  • Standard File SaveAs... and Open...
  • Fractal Orbit Path Visualization
  • *
  • Comprehensive User Guide (built-in)
  • 35 LCARS Color Themes
  • Authentic Sound FX
  • Mute All Sound FX
  • Digital Clock
  • 12 Hour or 24 Hour Time
  • Stardates (2 types)
  • Cool Animations

Be sure and read the comprehensive user guide that is included with the app.

Have fun exploring FractalSpace.

Live Long and Prosper. \\//

Julia Trek Go To App Store
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