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Fractals

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In this application we create an procedural image by calculating the color of each pixel using fractal algorithms (Figure 1). Some of the most fascinating results produced by a dynamic system occur when we iterate a complex variable function instead of a real one. This is the case of Julia's sets. The source code is in folder /src/demo/fractals of the SDK distribution.

Capturing a viewer of Julia sets, Windows version. Capturing a viewer of Julia sets, macOS version.
Figure 1: Fractals application Windows and macOS version.
Capturing a viewer of Julia sets, Linux/Ubuntu version. Capturing a viewer of Julia sets, Raspbian version.
Figure 2: Ubuntu and Raspbian version.

Due to the large computational load of this algorithm we have divided the calculation into several threads (Figure 3). This problem is easily parallelizable simply by fractioning the image, because each pixel is obtained independently.

Image divided into four parts and four threads calculating each.
Figure 3: Collaboration of several threads.
Listing 1: demo/fractals/fractals.c
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/* Multi-threaded fractals */

#include "nappgui.h"

typedef struct _app_t App;
typedef struct _thdata_t ThData;

struct _app_t
{
    Window *window;
    ImageView *view;
    Label *time_label;
    Clock *clock;
    uint32_t threads;
    bool_t vertical;
    real64_t fct;
};

struct _thdata_t
{
    real64_t fct;
    real64_t kreal;
    real64_t kimag;
    Pixbuf *pixbuf;
    uint32_t i;
    uint32_t j;
    uint32_t width;
    uint32_t height;
};

static const real64_t i_FCT = 2.85;
static const uint32_t i_ITERATIONS = 512;
static const uint32_t i_WIDTH = 601;
static const uint32_t i_HEIGHT = 601;

/*---------------------------------------------------------------------------*/

static uint32_t i_inset(real64_t zreal, real64_t zimag, real64_t creal, real64_t cimag)
{
    uint32_t i;
    for(i = 0; i < i_ITERATIONS; ++i) 
    {
        real64_t ztmp, zdist;
        ztmp = zreal * zreal - zimag * zimag;
        zimag = zreal * zimag + zreal * zimag;
        zreal = ztmp;
        zreal = zreal + creal;
        zimag = zimag + cimag;
        zdist = zimag * zimag  + zreal * zreal;
        if (zdist > 3) 
            return i;
    }

    return 0;
}

/*---------------------------------------------------------------------------*/

static uint32_t i_julia_thread(ThData *data)
{
    real64_t fct = data->fct;
    uint32_t imgwidth = pixbuf_width(data->pixbuf);
    real64_t freal = fct / imgwidth;
    real64_t fimag = fct / pixbuf_height(data->pixbuf);
    real64_t kreal = data->kreal;
    real64_t kimag = data->kimag;
    uint32_t val;
    real64_t creal, cimag;
    register uint32_t stj = data->j;
    register uint32_t edj = data->j + data->height;
    register uint32_t sti = data->i;
    register uint32_t edi = data->i + data->width;
    register uint32_t i, j;

    for(j = stj; j < edj; ++j)
    {
        cimag = fimag * j - (fct / 2);

        for(i = sti; i < edi; ++i)
        {
            creal = freal * i - (fct / 2);
            val = i_inset(creal, cimag, kreal, kimag);
            if (val > 0)
            {
                uint8_t n_val = val % 255;
                if ( val < ( i_ITERATIONS >> 1 ) )
                    val = color_rgb((uint8_t)(n_val << 2), (uint8_t)(n_val << 3), (uint8_t)(n_val << 4));
                else
                    val = color_rgb((uint8_t)(n_val << 4), (uint8_t)(n_val << 2), (uint8_t)(n_val << 5));
            }
            else
            {
                val = kCOLOR_BLACK;
            }

            pixbuf_set(data->pixbuf, i, j, val);
        }
    }

    return 5;
}

/*---------------------------------------------------------------------------*/

static void i_julia(const uint32_t nthreads, const bool_t vertical, const real64_t fct, const real64_t kreal, const real64_t kimag, Pixbuf *pixbuf)
{
    ThData data[8];
    uint32_t width = pixbuf_width(pixbuf);
    uint32_t height = pixbuf_height(pixbuf);
    data[0].fct = fct;
    data[0].kreal = kreal;
    data[0].kimag = kimag;
    data[0].pixbuf = pixbuf;

    if (nthreads == 1)
    {
        data[0].i = 0;
        data[0].j = 0;
        data[0].width = width;
        data[0].height = height;
        i_julia_thread(&data[0]);
    }
    else
    {
        Thread *thread[8];

        register uint32_t i;
        if (vertical == TRUE)
        {
            uint32_t twidth = width / nthreads;
            for (i = 0; i < nthreads; ++i)
            {
                data[i] = data[0];
                data[i].i = i * twidth;
                data[i].j = 0;
                data[i].width = twidth;
                data[i].height = height;
            }

            data[nthreads-1].width += (width - (twidth * nthreads));
        }
        else
        {
            uint32_t theight = height / nthreads;
            for (i = 0; i < nthreads; ++i)
            {
                data[i] = data[0];
                data[i].i = 0;
                data[i].j = i * theight;
                data[i].width = width;
                data[i].height = theight;
            }

            data[nthreads-1].height += (height - (theight * nthreads));
        }

        for (i = 0; i < nthreads; ++i)
            thread[i] = bthread_create(i_julia_thread, &data[i], ThData);

        for (i = 0; i < nthreads; ++i)
        {
            uint32_t thid = bthread_wait(thread[i]);
            cassert_unref(thid == 5, thid);
            bthread_close(&thread[i]);
        }
    }
}

/*---------------------------------------------------------------------------*/

static void i_image(App *app)
{
    Pixbuf *pixbuf = pixbuf_create(i_WIDTH, i_HEIGHT, ekRGBA32);
    real64_t rfactor = app->fct / i_WIDTH;
    real64_t ifactor = app->fct / i_HEIGHT;
    real64_t kreal = rfactor * 307 - 2;
    real64_t kimag = ifactor * 184 - 1.4;
    Image *image = NULL;
    real64_t timems;
    String *str;
    clock_reset(app->clock);
    i_julia(app->threads, app->vertical, app->fct, kreal, kimag, pixbuf);
    timems = 1000. * clock_elapsed(app->clock);
    str = str_printf("%.3f milliseconds", timems);
    label_text(app->time_label, tc(str));
    str_destroy(&str);
    image = image_from_pixbuf(pixbuf, NULL);
    imageview_image(app->view, image);
    image_destroy(&image);
    pixbuf_destroy(&pixbuf);
}

/*---------------------------------------------------------------------------*/

static void i_OnSlider(App *app, Event *e)
{
    const EvSlider *p = event_params(e, EvSlider);
    real64_t st = i_FCT - 1;
    real64_t ed = i_FCT + 1;
    app->fct = ((ed - st) * p->pos) + st;
    i_image(app);
}

/*---------------------------------------------------------------------------*/

static void i_OnThreads(App *app, Event *e)
{
    const EvButton *p = event_params(e, EvButton);
    switch(p->index) {
    case 0: app->threads = 1; break;
    case 1: app->threads = 2; break;
    case 2: app->threads = 3; break;
    case 3: app->threads = 4; break;
    case 4: app->threads = 8; break; }
    i_image(app);
}

/*---------------------------------------------------------------------------*/

static void i_OnVertical(App *app, Event *e)
{
    const EvButton *p = event_params(e, EvButton);
    app->vertical = p->index == 0 ? TRUE : FALSE;
    i_image(app);
}

/*---------------------------------------------------------------------------*/

static Panel *i_panel(App *app)
{
    Panel *panel = panel_create();
    Layout *layout1 = layout_create(1, 3);
    Layout *layout2 = layout_create(5, 1);
    Label *label1 = label_create();
    Label *label2 = label_create();
    PopUp *popup = popup_create();
    Slider *slider = slider_create();
    Button *button1 = button_radio();
    Button *button2 = button_radio();
    ImageView *view = imageview_create();
    label_text(label1, "Threads:");
    popup_add_elem(popup, "1", NULL);
    popup_add_elem(popup, "2", NULL);
    popup_add_elem(popup, "3", NULL);
    popup_add_elem(popup, "4", NULL);
    popup_add_elem(popup, "8", NULL);
    popup_selected(popup, 0);
    popup_OnSelect(popup, listener(app, i_OnThreads, App));
    slider_value(slider, .5f);
    slider_OnMoved(slider, listener(app, i_OnSlider, App));
    button_text(button1, "Vert");
    button_text(button2, "Hotz");
    button_state(button1, ekON);
    button_OnClick(button1, listener(app, i_OnVertical, App));
    imageview_size(view, s2di(i_WIDTH, i_HEIGHT));
    layout_slider(layout1, slider, 0, 0);
    layout_label(layout2, label1, 0, 0);
    layout_popup(layout2, popup, 1, 0);
    layout_button(layout2, button1, 2, 0);
    layout_button(layout2, button2, 3, 0);
    layout_label(layout2, label2, 4, 0);
    layout_halign(layout2, 4, 0, ekJUSTIFY);
    layout_hexpand(layout2, 4);
    layout_layout(layout1, layout2, 0, 1);
    layout_imageview(layout1, view, 0, 2);
    layout_vmargin(layout1, 1, 5);
    layout_margin2(layout2, 0, 5);
    layout_hmargin(layout2, 0, 5);
    layout_hmargin(layout2, 1, 10);
    layout_hmargin(layout2, 2, 5);
    layout_hmargin(layout2, 3, 15);
    panel_layout(panel, layout1);
    app->fct = i_FCT;
    app->threads = 1;
    app->vertical = TRUE;
    app->view = view;
    app->time_label = label2;
    return panel;
}

/*---------------------------------------------------------------------------*/

static void i_OnClose(App *app, Event *e)
{
    osapp_finish();
    unref(app);
    unref(e);
}

/*---------------------------------------------------------------------------*/

static App *i_create(void)
{
    App *app = heap_new0(App);
    Panel *panel = i_panel(app);
    app->window = window_create(ekWNSTD, &panel);
    app->clock = clock_create(0);
    i_image(app);
    window_title(app->window, "Fractals");
    window_origin(app->window, v2df(500, 200));
    window_OnClose(app->window, listener(app, i_OnClose, App));
    window_show(app->window);
    return app;
}

/*---------------------------------------------------------------------------*/

static void i_destroy(App **app)
{
    window_destroy(&(*app)->window);
    clock_destroy(&(*app)->clock);
    heap_delete(app, App);
}

/*---------------------------------------------------------------------------*/

#include "osmain.h"
osmain(i_create, i_destroy, "", App)
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